HDAT9600 Final Assignment
Please see course outline / ‘Announcements’ for submission deadline
Meg Stevens, Maathumai Ranjan, Victor Hui, Haran Nathan
insert date of completion here
Instructions
This file (hdat9600_final_assignment.Rmd) is the R Markdown document in which you need to complete your HDAT9600 final assignment. This assignment is assessed and will count for 30% of the total course marks. The assignment comprises two tasks worth 15 marks each. The first task will focus on logistic regression, and the second task will focus on survival analysis. There is no word limit, but a report of about 10 pages in length when printed (except that it will not be printed) is appropriate.
Don’t hesitate to ask the course convenor for help via OpenLearning. The course instructor are happy to point you in the right direction and to make suggestions, but they won’t, of course, complete your assignments for you!
Data for this assignment
The data used for this assignment consist of records from Intensive Care Unit (ICU) hospital stays in the USA. All patients were adults who were admitted for a wide variety of reasons. ICU stays of less than 48 hours have been excluded.
The source data for the assignment are data made freely available for the 2012 MIT PhysioNet/Computing for Cardiology Challenge. Details are provided here. Training Set A data have been used. The original data has been modified and assembled to suit the purpose of this assignment. While not required for the purposes of this assignment, full details of the preparatory work can be found in the hdat9600_final_assignment_data_preparation file.
The dataframe consists of 120 variables, which are defined as follows:
Patient Descriptor Variables
Outcome Variables
Clinical Variables
Use the hyperlinks below to find out more about the clinical meaning of each variable. The first two clinical variables are summary scores that are used to assess patient condition and risk.
The following 36 clinical measures were assessed at multiple timepoints during each patient’s ICU stay. For each of the 36 clinical measures, you are given 3 summary variables: a) The minimum value during the first 24 hours in ICU (_min), b) The maximum value during the first 24 hours in ICU (_max), and c) The difference between the mean and the most extreme values during the first 24 hours in ICU (_diff). For example, for the clinical measure Cholesterol, these three variables are labelled ‘Cholesterol_min’, ‘Cholesterol_max’, and ‘Cholesterol_diff’.
Accessing the Data
The data frame can be loaded with the following code:
# import required packages
library(ggplot2)
library(gridExtra)
library(magrittr)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:gridExtra':
##
## combine## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(survival)
library(eha)
library(stringi)
library(bshazard)## Loading required package: splines## Loading required package: Epilibrary(survminer)## Loading required package: ggpubr# Getting the path of your current open file
# Extra code to ensure this file imports data in local directory
library(rstudioapi)
current_path <- rstudioapi::getActiveDocumentContext()$path
setwd(dirname(current_path ))
# import data
icu_patients_df0 <- readRDS("icu_patients_df0.rds")
icu_patients_df1 <- readRDS("icu_patients_df1.rds")Note: icu_patients_df1 is an imputed (i.e. missing values are ‘derived’) version of icu_patients_df0. This assignment does not concern the methods used for imputation.
Task 1 (15 marks)
In this task, you are required to develop a logistic regression model using the icu_patients_df1 data set which adequately explains or predicts the in_hospital_death variable as the outcome using a subset of the available predictor variables. You should fit a series of models, evaluating each one, before you present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge. It is perfectly acceptable to include predictor variables in your final model which are not statistically significant, as long as you justify their inclusion on medical or physiological grounds (you will not be marked down if your medical justification is not exactly correct or complete, but do you best). Aim for between five and ten predictor variables (slightly more or fewer is OK). You should assess each model you consider for goodness of fit and other relevant statistics to help you choose between them. For your final model, present a set of diagnostic statistics and/or charts and comment on them. You don’t need to do an exhaustive exploratory data analysis of all the variables in the data set, but you should examine those variables that you use in your model. Finally, re-fit your final model to the unimputed data frame (icu_patients_df0.rds) and comment on any differences you find compared to the same model fitted to the imputed data.
Hints
Select an initial subset of explanatory variables that you will use to predict the risk of in-hospital death. Justify your choice.
Conduct basic exploratory data analysis on your variables of choice.
Fit appropriate univariate logistic regression models.
To select a subset of explanatory variables, we have examined the SAPS1 score and the SOFA scores included in the dataset in more detail to ascertain which variables could be logically associated with increased mortality and poor survival. We have also assessed the clinical measures used to calculate the APACHE score which is another commonly used measure in ICU risk prediction models.
- Write a paragraph summarising the most important findings of your final model. Include the most important values from the statistical output, and a simple clinical interpretation.
Task 1 Response:
Select an initial subset of explanatory variables:
The purpose of this task is to understand the impact of information collected during the first 24 hours of an ICU stay on in-hospital mortality of the ICU population.
To select a subset of explanatory variables, we have examined the SAPS1 score and the SOFA scores included in the dataset in more detail to ascertain which variables could be logically associated with increased mortality and poor survival. We have also assessed the clinical measures used to calculate the APACHE score which is another commonly used measure in ICU risk prediction models.
SAPS1 - Simplified Acute Physiology Score is a measure of the severity of disease for patients admitted to ICU. The following measures increases the SAPS1 score:
- Advanced Age
- Low and high Heart Rate
- Low and high Systolic Blood Pressure
- High Temperature
- Low Glasgow Coma Scale (However it is most meaningful to use the highest GCS score available for prognostication)
- Mechanical Ventilation or CPAP
- High PaO2/ FiO2 ratio (It is likely that highest FiO2 is administered during lowest PaO2)
- Low Urine Output
- High Blood Urea Nitrogen
- Low or High Sodium
- Low or high Potassium
- Low Bicarbonate
- High Bilirubin
- Low or High White Blood Cell
- Chronic diseases
- Type of admission (ie ICU Type)
SOFA - sequential organ failure assessment is a predictor of ICU mortality. The following measures increase the SOFA score:
- Elevated PaO2/ FiO2 ratio-
- Reduced GCS - Nervous system
- Reduced MAP - Cardiovascular system
- Administration of vasopressors - Cardiovascular system
- High Bilirubin - Liver
- Low Platelets - Coagulation
- High Creatinine - Kidneys
- Low Urine - Kidneys
The APACHE score is commonly used validated risk score for ICU risk prediction. The variables that increase the APACHE score include:
- Advanced Age
- High or Low Temperature
- High or Low MAP
- High or Low HR
- High or Low Respiratory Rate
- High PaO2/FiO2 ratio
- High or Low pH
- High or Low Na
- High or Low K
- High Creatinine
- High or low HCT
- High or Low WBC
In the exploratory analysis, we include variables that will increase SOFA, SAPS or APACHE scores (note that higher SOFA, SAPS and APACHE scores are associated with higher risk of mortality). For example, increased BUN and reduced HCO3 will increase the SAPS score, therefore we will include BUN_max (but not BUN_min and BUN_diff) and HCO3_min (but not HCO3_max and HCO3_diff). Where both extremes of a variable will increase the risk score, both min and max variables will be included.
Other factors known to be associated with morbidity/ mortality not included in risk scores: * Height/ weight - Body composition/ BMI is associated with mortality and survival * Gender - Males are typically associated with high risk of mortality * Glucose - high and low Glucose levels are associated with pathology * Troponin T and I - high troponin results (cardiac biomarkers) associated with morbidity and mortality * Lactate - elevated lactate is associated with poor organ perfusion and ICU morbidity/ mortality * Albumin - reduced albumin is associated with poor clinical outcomes
Therefore, the initial subset of explanatory variables we have chosen for this task are:
DEMOGRAPHIC VARIABLES:
* Age
* Gender
* ICUType
* Height
* Weight_max
CLINICAL VARIABLES:
* Albumin_min
* Bilirubin_max
* BUN_max
* Creatinine_max
* GCS_min
* Glucose_min and Glucose_max
* HCO3_min
* HR_min and HR_max
* K_min and K_max
* Lactate_max
* MAP_min
* Na_min and Na_max
* NISysABP_min and NISysABP_max
* Platelets_min
* FiO2_max and PaO2_min - included as PFratio= PaO2_min/ FiO2_max
* pH_min and pH_max
* RespRate_min and RespRate_max
* Temp_min and Temp_max
* TroponinI_max
* TroponinT_max
* Urine_min
* WBC_min and WBC_max
Basic initial exploratory data analysis (EDA):
# create new variable PF ratio as part of our list of variables to include
icu_patients_df1$PFratio<-icu_patients_df1$PaO2_min/icu_patients_df1$FiO2_max
icu_patients_df0$PFratio<-icu_patients_df0$PaO2_min/icu_patients_df0$FiO2_max
# create a vector of the variables chosen to explore
explore_vars <- c('Age', 'Gender', 'ICUType', 'Height', 'Weight_max',
'Albumin_min', 'Bilirubin_max', 'BUN_max', 'Creatinine_max',
'GCS_min', 'Glucose_min', 'Glucose_max', 'HCO3_min', 'HR_min',
'HR_max', 'K_min', 'K_max', 'Lactate_max', 'MAP_min',
'Na_min', 'Na_max', 'NISysABP_min', 'NISysABP_max',
'Platelets_min', 'PFratio', 'pH_min', 'pH_max',
'RespRate_min', 'RespRate_max', 'Temp_min', 'Temp_max',
'TroponinI_max', 'TroponinT_max', 'Urine_min', 'WBC_min',
'WBC_max')
# examine the summary output for each chosen variable
summary(icu_patients_df1[,explore_vars])## Age Gender ICUType
## Min. :16.00 Female: 913 Coronary Care Unit :297
## 1st Qu.:52.00 Male :1148 Cardiac Surgery Recovery Unit:448
## Median :67.00 Medical ICU :788
## Mean :64.41 Surgical ICU :528
## 3rd Qu.:78.00
## Max. :90.00
##
## Height Weight_max Albumin_min Bilirubin_max
## Min. : 13.0 Min. : 34.60 Min. :1.100 Min. : 0.100
## 1st Qu.:162.6 1st Qu.: 66.00 1st Qu.:2.600 1st Qu.: 0.400
## Median :170.2 Median : 80.00 Median :3.000 Median : 0.700
## Mean :170.0 Mean : 82.66 Mean :3.012 Mean : 1.739
## 3rd Qu.:177.8 3rd Qu.: 94.55 3rd Qu.:3.500 3rd Qu.: 1.300
## Max. :426.7 Max. :230.00 Max. :5.300 Max. :45.900
## NA's :992 NA's :146
## BUN_max Creatinine_max GCS_min Glucose_min
## Min. : 3.00 Min. : 0.200 Min. : 3.000 Min. : 24.0
## 1st Qu.: 14.00 1st Qu.: 0.800 1st Qu.: 3.000 1st Qu.: 98.0
## Median : 20.00 Median : 1.000 Median : 8.000 Median :117.0
## Mean : 27.48 Mean : 1.499 Mean : 8.773 Mean :124.8
## 3rd Qu.: 33.00 3rd Qu.: 1.500 3rd Qu.:14.000 3rd Qu.:141.0
## Max. :197.00 Max. :22.000 Max. :15.000 Max. :632.0
##
## Glucose_max HCO3_min HR_min HR_max
## Min. : 39.0 Min. : 5.00 Min. : 0.00 Min. : 44.0
## 1st Qu.: 117.0 1st Qu.:20.00 1st Qu.: 61.00 1st Qu.: 91.0
## Median : 141.0 Median :23.00 Median : 71.00 Median :104.0
## Mean : 163.3 Mean :22.43 Mean : 71.99 Mean :106.6
## 3rd Qu.: 180.0 3rd Qu.:25.00 3rd Qu.: 81.00 3rd Qu.:119.0
## Max. :1143.0 Max. :44.00 Max. :126.00 Max. :300.0
##
## K_min K_max Lactate_max MAP_min
## Min. :1.80 Min. : 2.500 Min. : 0.400 Min. : 1.00
## 1st Qu.:3.50 1st Qu.: 4.000 1st Qu.: 1.500 1st Qu.: 55.00
## Median :3.90 Median : 4.300 Median : 2.200 Median : 61.00
## Mean :3.95 Mean : 4.419 Mean : 2.773 Mean : 62.76
## 3rd Qu.:4.30 3rd Qu.: 4.700 3rd Qu.: 3.200 3rd Qu.: 70.00
## Max. :6.90 Max. :22.900 Max. :29.300 Max. :265.00
##
## Na_min Na_max NISysABP_min NISysABP_max Platelets_min
## Min. : 98 Min. :112.0 Min. : 4.00 Min. : 78.0 Min. : 9.0
## 1st Qu.:136 1st Qu.:137.0 1st Qu.: 83.00 1st Qu.:121.0 1st Qu.:126.0
## Median :138 Median :140.0 Median : 95.00 Median :138.0 Median :184.0
## Mean :138 Mean :139.8 Mean : 96.55 Mean :140.5 Mean :197.9
## 3rd Qu.:141 3rd Qu.:142.0 3rd Qu.:108.00 3rd Qu.:156.0 3rd Qu.:246.0
## Max. :160 Max. :177.0 Max. :234.00 Max. :274.0 Max. :891.0
## NA's :453 NA's :453
## PFratio pH_min pH_max RespRate_min RespRate_max
## Min. : 24 Min. :3.000 Min. :7.150 Min. : 4.00 Min. :13.00
## 1st Qu.: 85 1st Qu.:7.280 1st Qu.:7.380 1st Qu.:12.00 1st Qu.:24.00
## Median : 122 Median :7.340 Median :7.420 Median :14.00 Median :27.00
## Mean : 154 Mean :7.327 Mean :7.418 Mean :14.25 Mean :29.12
## 3rd Qu.: 188 3rd Qu.:7.390 3rd Qu.:7.460 3rd Qu.:17.00 3rd Qu.:33.00
## Max. :1150 Max. :7.630 Max. :7.690 Max. :24.00 Max. :98.00
##
## Temp_min Temp_max TroponinI_max TroponinT_max
## Min. :24.20 Min. :35.40 Min. : 0.30 Min. : 0.0100
## 1st Qu.:35.60 1st Qu.:37.10 1st Qu.: 2.60 1st Qu.: 0.0600
## Median :36.10 Median :37.60 Median : 7.80 Median : 0.1700
## Mean :36.01 Mean :37.69 Mean :11.83 Mean : 0.9079
## 3rd Qu.:36.60 3rd Qu.:38.20 3rd Qu.:17.60 3rd Qu.: 0.8000
## Max. :38.30 Max. :42.10 Max. :43.40 Max. :24.4600
##
## Urine_min WBC_min WBC_max
## Min. : 0.00 Min. : 0.10 Min. : 0.10
## 1st Qu.: 0.00 1st Qu.: 7.60 1st Qu.: 9.30
## Median : 20.00 Median : 10.40 Median : 12.30
## Mean : 34.55 Mean : 11.51 Mean : 13.95
## 3rd Qu.: 36.00 3rd Qu.: 14.10 3rd Qu.: 16.90
## Max. :600.00 Max. :128.30 Max. :155.60
## # Write a function to plot box plots for each variable by in_hospital_death
boxplot_eda <- function(variable){
plot <- ggplot(data=icu_patients_df1,
mapping = aes(x = in_hospital_death=="1",
y = icu_patients_df1[,variable])) +
geom_boxplot() +
labs(title=paste('Box plot of',variable),
x='In hospital death', y=variable)
return(plot)
}
# Continuous variables EDA and their interpretation
# continuous variables from the list of initial subset of explanatory variables
cont_vars <- c('Age', 'Height', 'Weight_max', 'Albumin_min', 'Bilirubin_max',
'BUN_max', 'Creatinine_max', 'GCS_min', 'Glucose_min',
'Glucose_max', 'HCO3_min', 'HR_min', 'HR_max', 'K_min', 'K_max',
'Lactate_max', 'MAP_min', 'Na_min', 'Na_max', 'NISysABP_min',
'NISysABP_max', 'Platelets_min', 'PFratio', 'pH_min', 'pH_max',
'RespRate_min', 'RespRate_max', 'Temp_min', 'Temp_max',
'TroponinI_max', 'TroponinT_max', 'Urine_min', 'WBC_min', 'WBC_max')
# Loop through the continuous variables and produce box plots using the boxplot_eda() function
b <- list() # initialise an empty list to store the plots in
for(i in 1:length(cont_vars)){
b[[i]] <- boxplot_eda(cont_vars[i])
}
# arrange the list of plots in a 12 row grid using grid.arrange() from package{gridExtra}
do.call(grid.arrange, c(b, nrow = 12))## Warning: Removed 992 rows containing non-finite values (stat_boxplot).## Warning: Removed 146 rows containing non-finite values (stat_boxplot).## Warning: Removed 453 rows containing non-finite values (stat_boxplot).
## Warning: Removed 453 rows containing non-finite values (stat_boxplot).
# Patients who died had higher SAPS1 and SOFA scores
ggplot(data=icu_patients_df1,
mapping = aes(x = in_hospital_death=="1", y = SAPS1)) + geom_boxplot() +
labs(title=paste('Box plot of SAPS1 scores'),
x='In hospital death', y='SAPS1 score')## Warning: Removed 96 rows containing non-finite values (stat_boxplot).
ggplot(data=icu_patients_df1,
mapping = aes(x = in_hospital_death=="1", y = SOFA)) + geom_boxplot() +
labs(title=paste('Box plot of SOFA scores'),
x='In hospital death', y='SOFA score')
### Categorical variables EDA and their interpretation ###
# cardiac surgery recovery unit have a smaller death circle compared to the other 3 ICU units
# ie less proportion of in hospital deaths compared to alive
icutype_plot <- ggplot(data=icu_patients_df1,
mapping = aes(x = in_hospital_death=="1", y = ICUType)) +
geom_count(aes(size = after_stat(prop), group = ICUType)) +
scale_size_area(max_size = 10) +
labs(title=paste('Proportion of patients by ICU type'),
x='In hospital death', size='Proportion of patients')
# difficult to say, roughly same amount of men/women died as a proportion of the alive group
gender_plot <- ggplot(data=icu_patients_df1,
mapping = aes(x = in_hospital_death=="1", y = Gender)) +
geom_count(aes(size = after_stat(prop), group = ICUType)) +
scale_size_area(max_size = 20) +
labs(title=paste('Proportion of patients by gender'),
x='In hospital death', size='Proportion of patients')
# arrange the categorical variable plots side-by-side
grid.arrange(icutype_plot, gender_plot, nrow=1)
EDA Findings:
There are 2061 unique individuals in the dataset. Of these, 913 are female (44%) and 1148 are male (56%).
There were 297 deaths out of 2061 observations, which is a risk rate of 14.4% (not an uncommon event).
Medical ICU accounted for 38% of individuals, 26% in Surgical ICU, 24% in Cardiac Surgery recovery Unit and 14% in the Coronary Care unit.
The following variables have a large proportion of missing observations:
Weight_max- 146 missing observationsHeight- 992 missing observationsNISysABP_min&NISysABP_max- 453 missing observations
Proportion of in hospital deaths were observed for each variable:
- Those that died had higher SAPS1 and SOFA scores.
- Females had higher proportion of deaths than males.
- Medical ICU had a greatest rate of mortality, whereas Cardiac Surgery recovery unit had the lowest porportion of deaths.
- Higher age in those that died
- Higher min albumin in those that died
- Slightly higher max bilirubin in those that died
- Higher max (BUN) urea in those that died
- Higher max creatinine in those that died
- Lower GCS min in those that died
- Similar min glucose in both groups
- Slightly higher max glucose in those that died
- Lower min HCO3 in those that died
- Similar min HR in both groups
- Slightly higher max HR in those that died
- Similar min K in both groups
- Similar max K in both groups
- Slightly higher max lactate in those that died
- Similar min MAP in both groups
- Similar min Na in both groups
- Similar max Na in both groups
- Slightly lower min NISysABP in those that died
- Similar max NISysABP in both groups
- Similar min platelets in both groups
- Similar PF ratio in both groups
- Similar min pH in both groups - one extreme outlier
- Similar pH max in both groups
- Higher min RR in those that died
- Higher max RR in those that died
- Similar min temp in both groups
- Similar max temp in both groups
- Similar max troponinI in both groups
- Similar max troponinT in both groups
- Similar min urine in both groups
- Slightly higher min WBC in those that died
- Slightly higher max WBC in those that died
Univariate logistic regression models:
# Univariate logistic regression comparisons for all initial selected variables
age_glm <- glm(in_hospital_death ~ Age, data=icu_patients_df1, family="binomial")
summary(age_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Age, family = "binomial", data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7522 -0.6264 -0.5111 -0.3919 2.5135
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.761624 0.303337 -12.401 < 2e-16 ***
## Age 0.029376 0.004229 6.947 3.73e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1644.9 on 2059 degrees of freedom
## AIC: 1648.9
##
## Number of Fisher Scoring iterations: 5gender_glm <- glm(in_hospital_death ~ Gender, data=icu_patients_df1, family="binomial")
summary(gender_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ Gender, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5612 -0.5612 -0.5553 -0.5553 1.9728
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.76894 0.09381 -18.856 <2e-16 ***
## GenderMale -0.02281 0.12615 -0.181 0.856
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1699.7 on 2059 degrees of freedom
## AIC: 1703.7
##
## Number of Fisher Scoring iterations: 4icuType_glm <- glm(in_hospital_death ~ ICUType, data=icu_patients_df1, family="binomial")
summary(icuType_glm) # cardiac surgery recovery unit is significant##
## Call:
## glm(formula = in_hospital_death ~ ICUType, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6402 -0.6402 -0.5615 -0.3458 2.3861
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.6463 0.1576 -10.443 < 2e-16 ***
## ICUTypeCardiac Surgery Recovery Unit -1.1407 0.2563 -4.451 8.55e-06 ***
## ICUTypeMedical ICU 0.1653 0.1824 0.906 0.365
## ICUTypeSurgical ICU -0.1214 0.2001 -0.607 0.544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1655.3 on 2057 degrees of freedom
## AIC: 1663.3
##
## Number of Fisher Scoring iterations: 5maxWeight_glm <- glm(in_hospital_death ~ Weight_max, data=icu_patients_df1, family="binomial")
summary(maxWeight_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Weight_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6460 -0.5846 -0.5605 -0.5231 2.1768
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.246092 0.242568 -5.137 2.79e-07 ***
## Weight_max -0.006212 0.002912 -2.133 0.0329 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1599.4 on 1913 degrees of freedom
## (146 observations deleted due to missingness)
## AIC: 1603.4
##
## Number of Fisher Scoring iterations: 4minAlbumin_glm <- glm(in_hospital_death ~ Albumin_min, data=icu_patients_df1, family="binomial")
summary(minAlbumin_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Albumin_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7948 -0.5887 -0.5385 -0.4595 2.2842
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.36392 0.29389 -1.238 0.216
## Albumin_min -0.48186 0.09987 -4.825 1.4e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1676.0 on 2059 degrees of freedom
## AIC: 1680
##
## Number of Fisher Scoring iterations: 4maxBili_glm <- glm(in_hospital_death ~ Bilirubin_max, data=icu_patients_df1, family="binomial")
summary(maxBili_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Bilirubin_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3889 -0.5421 -0.5363 -0.5321 2.0174
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.90053 0.06866 -27.679 < 2e-16 ***
## Bilirubin_max 0.05692 0.01135 5.013 5.35e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1676.8 on 2059 degrees of freedom
## AIC: 1680.8
##
## Number of Fisher Scoring iterations: 4maxUrea_glm <- glm(in_hospital_death ~ BUN_max, data=icu_patients_df1, family="binomial")
summary(maxUrea_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ BUN_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0462 -0.5269 -0.4789 -0.4443 2.2309
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.492189 0.103693 -24.034 <2e-16 ***
## BUN_max 0.022610 0.002347 9.634 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1607.3 on 2059 degrees of freedom
## AIC: 1611.3
##
## Number of Fisher Scoring iterations: 4maxCr_glm <- glm(in_hospital_death ~ Creatinine_max, data=icu_patients_df1, family="binomial")
summary(maxCr_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Creatinine_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8627 -0.5433 -0.5270 -0.5151 2.0633
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.05087 0.08430 -24.328 < 2e-16 ***
## Creatinine_max 0.16325 0.03135 5.208 1.91e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1674.4 on 2059 degrees of freedom
## AIC: 1678.4
##
## Number of Fisher Scoring iterations: 4minGCS_glm <- glm(in_hospital_death ~ GCS_min, data=icu_patients_df1, family="binomial")
summary(minGCS_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ GCS_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6238 -0.6238 -0.5394 -0.4853 2.0964
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.40261 0.12298 -11.405 < 2e-16 ***
## GCS_min -0.04514 0.01317 -3.426 0.000612 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1687.7 on 2059 degrees of freedom
## AIC: 1691.7
##
## Number of Fisher Scoring iterations: 4minGlu_glm <- glm(in_hospital_death ~ Glucose_min, data=icu_patients_df1, family="binomial")
summary(minGlu_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ Glucose_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7799 -0.5613 -0.5522 -0.5428 2.0271
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.967537 0.171241 -11.490 <2e-16 ***
## Glucose_min 0.001476 0.001253 1.178 0.239
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1698.4 on 2059 degrees of freedom
## AIC: 1702.4
##
## Number of Fisher Scoring iterations: 4maxGlu_glm <- glm(in_hospital_death ~ Glucose_max, data=icu_patients_df1, family="binomial")
summary(maxGlu_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Glucose_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4117 -0.5572 -0.5343 -0.5162 2.0872
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.1865370 0.1202802 -18.179 < 2e-16 ***
## Glucose_max 0.0023817 0.0005819 4.093 4.25e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1684.2 on 2059 degrees of freedom
## AIC: 1688.2
##
## Number of Fisher Scoring iterations: 4minHCO3_glm <- glm(in_hospital_death ~ HCO3_min, data=icu_patients_df1, family="binomial")
summary(minHCO3_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ HCO3_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9781 -0.5748 -0.5165 -0.4634 2.6504
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.10497 0.29323 -0.358 0.72
## HCO3_min -0.07675 0.01345 -5.705 1.17e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1666.8 on 2059 degrees of freedom
## AIC: 1670.8
##
## Number of Fisher Scoring iterations: 4minHR_glm <- glm(in_hospital_death ~ HR_min, data=icu_patients_df1, family="binomial")
summary(minHR_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ HR_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6235 -0.5656 -0.5528 -0.5390 2.1087
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.108733 0.301434 -6.996 2.64e-12 ***
## HR_min 0.004520 0.004052 1.115 0.265
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1698.4 on 2059 degrees of freedom
## AIC: 1702.4
##
## Number of Fisher Scoring iterations: 4maxHR_glm <- glm(in_hospital_death ~ HR_max, data=icu_patients_df1, family="binomial")
summary(maxHR_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ HR_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1194 -0.5733 -0.5402 -0.5067 2.1517
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.707555 0.303251 -8.928 < 2e-16 ***
## HR_max 0.008565 0.002707 3.164 0.00156 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1689.9 on 2059 degrees of freedom
## AIC: 1693.9
##
## Number of Fisher Scoring iterations: 4minK_glm <- glm(in_hospital_death ~ K_min, data=icu_patients_df1, family="binomial")
summary(minK_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ K_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6024 -0.5647 -0.5546 -0.5447 2.0345
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.47413 0.42361 -3.480 0.000502 ***
## K_min -0.07804 0.10660 -0.732 0.464083
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1699.1 on 2059 degrees of freedom
## AIC: 1703.1
##
## Number of Fisher Scoring iterations: 4maxK_glm <- glm(in_hospital_death ~ K_max, data=icu_patients_df1, family="binomial")
summary(maxK_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ K_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2402 -0.5620 -0.5512 -0.5380 2.0561
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.24634 0.28233 -7.956 1.77e-15 ***
## K_max 0.10449 0.06153 1.698 0.0895 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1697.0 on 2059 degrees of freedom
## AIC: 1701
##
## Number of Fisher Scoring iterations: 4maxLactate_glm <- glm(in_hospital_death ~ Lactate_max, data=icu_patients_df1, family="binomial")
summary(maxLactate_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Lactate_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.1726 -0.5544 -0.5200 -0.4939 2.1212
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.1932 0.1005 -21.820 < 2e-16 ***
## Lactate_max 0.1372 0.0244 5.625 1.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1669.5 on 2059 degrees of freedom
## AIC: 1673.5
##
## Number of Fisher Scoring iterations: 4minMAP_glm <- glm(in_hospital_death ~ MAP_min, data=icu_patients_df1, family="binomial")
summary(minMAP_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ MAP_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6583 -0.5674 -0.5551 -0.5341 2.4214
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.413112 0.257434 -5.489 4.04e-08 ***
## MAP_min -0.005926 0.004051 -1.463 0.143
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1697.4 on 2059 degrees of freedom
## AIC: 1701.4
##
## Number of Fisher Scoring iterations: 4minNa_glm <- glm(in_hospital_death ~ Na_min, data=icu_patients_df1, family="binomial")
summary(minNa_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Na_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9061 -0.5706 -0.5490 -0.5282 2.2298
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.04227 1.79129 1.140 0.2542
## Na_min -0.02776 0.01301 -2.133 0.0329 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1695.3 on 2059 degrees of freedom
## AIC: 1699.3
##
## Number of Fisher Scoring iterations: 4maxNa_glm <- glm(in_hospital_death ~ Na_max, data=icu_patients_df1, family="binomial")
summary(maxNa_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ Na_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6176 -0.5615 -0.5573 -0.5491 2.0760
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.664686 1.927556 -0.345 0.730
## Na_max -0.007993 0.013793 -0.580 0.562
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1699.4 on 2059 degrees of freedom
## AIC: 1703.4
##
## Number of Fisher Scoring iterations: 4minNISys_ABP_glm <- glm(in_hospital_death ~ NISysABP_min, data=icu_patients_df1, family="binomial")
summary(minNISys_ABP_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ NISysABP_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9728 -0.6135 -0.5731 -0.5005 2.3871
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.450605 0.328983 -1.370 0.170783
## NISysABP_min -0.012922 0.003466 -3.728 0.000193 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1403.1 on 1607 degrees of freedom
## Residual deviance: 1388.5 on 1606 degrees of freedom
## (453 observations deleted due to missingness)
## AIC: 1392.5
##
## Number of Fisher Scoring iterations: 4maxNISys_ABP_glm <- glm(in_hospital_death ~ NISysABP_max, data=icu_patients_df1, family="binomial")
summary(maxNISys_ABP_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ NISysABP_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6098 -0.5886 -0.5846 -0.5799 1.9414
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.7826689 0.3544507 -5.029 4.92e-07 ***
## NISysABP_max 0.0007759 0.0024679 0.314 0.753
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1403.1 on 1607 degrees of freedom
## Residual deviance: 1403.0 on 1606 degrees of freedom
## (453 observations deleted due to missingness)
## AIC: 1407
##
## Number of Fisher Scoring iterations: 3minPlt_glm <- glm(in_hospital_death ~ Platelets_min, data=icu_patients_df1, family="binomial")
summary(minPlt_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ Platelets_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6122 -0.5735 -0.5558 -0.5260 2.2141
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.5693181 0.1352494 -11.603 <2e-16 ***
## Platelets_min -0.0010963 0.0006322 -1.734 0.0829 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1696.6 on 2059 degrees of freedom
## AIC: 1700.6
##
## Number of Fisher Scoring iterations: 4maxPFratio_glm <- glm(in_hospital_death ~ PFratio, data=icu_patients_df1, family="binomial")
summary(maxPFratio_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ PFratio, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5806 -0.5687 -0.5595 -0.5398 2.1022
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.6790207 0.1148206 -14.623 <2e-16 ***
## PFratio -0.0006772 0.0006452 -1.049 0.294
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1698.5 on 2059 degrees of freedom
## AIC: 1702.5
##
## Number of Fisher Scoring iterations: 4minpH_glm <- glm(in_hospital_death ~ pH_min, data=icu_patients_df1, family="binomial")
summary(minpH_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ pH_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.9980 -0.5733 -0.5358 -0.4868 2.2874
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 19.5912 4.8996 3.998 6.37e-05 ***
## pH_min -2.9197 0.6699 -4.358 1.31e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1677.4 on 2059 degrees of freedom
## AIC: 1681.4
##
## Number of Fisher Scoring iterations: 4maxpH_glm <- glm(in_hospital_death ~ pH_max, data=icu_patients_df1, family="binomial")
summary(maxpH_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ pH_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6684 -0.5677 -0.5523 -0.5297 2.0743
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 9.3001 7.0197 1.325 0.185
## pH_max -1.4944 0.9469 -1.578 0.115
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1697.2 on 2059 degrees of freedom
## AIC: 1701.2
##
## Number of Fisher Scoring iterations: 4minRR_glm <- glm(in_hospital_death ~ RespRate_min, data=icu_patients_df1, family="binomial")
summary(minRR_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ RespRate_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7929 -0.5872 -0.5222 -0.4636 2.3445
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.01958 0.25802 -11.703 < 2e-16 ***
## RespRate_min 0.08432 0.01656 5.091 3.57e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1673.6 on 2059 degrees of freedom
## AIC: 1677.6
##
## Number of Fisher Scoring iterations: 4maxRR_glm <- glm(in_hospital_death ~ RespRate_max, data=icu_patients_df1, family="binomial")
summary(maxRR_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ RespRate_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4489 -0.5679 -0.5233 -0.4817 2.1771
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.835656 0.235885 -12.021 < 2e-16 ***
## RespRate_max 0.035250 0.007412 4.756 1.98e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1677.8 on 2059 degrees of freedom
## AIC: 1681.8
##
## Number of Fisher Scoring iterations: 4minTemp_glm <- glm(in_hospital_death ~ Temp_min, data=icu_patients_df1, family="binomial")
summary(minTemp_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Temp_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.8918 -0.5741 -0.5409 -0.4973 2.2040
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.4599 2.3473 3.178 0.00148 **
## Temp_min -0.2571 0.0654 -3.931 8.45e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1684.3 on 2059 degrees of freedom
## AIC: 1688.3
##
## Number of Fisher Scoring iterations: 4maxTemp_glm <- glm(in_hospital_death ~ Temp_max, data=icu_patients_df1, family="binomial")
summary(maxTemp_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ Temp_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6077 -0.5689 -0.5549 -0.5366 2.1386
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.60419 3.08152 0.521 0.603
## Temp_max -0.08988 0.08183 -1.098 0.272
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1698.5 on 2059 degrees of freedom
## AIC: 1702.5
##
## Number of Fisher Scoring iterations: 4maxTropI_glm <- glm(in_hospital_death ~ TroponinI_max, data=icu_patients_df1, family="binomial")
summary(maxTropI_glm) # NOT significant##
## Call:
## glm(formula = in_hospital_death ~ TroponinI_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5736 -0.5688 -0.5565 -0.5350 2.0415
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.719798 0.090789 -18.943 <2e-16 ***
## TroponinI_max -0.005329 0.005774 -0.923 0.356
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1698.8 on 2059 degrees of freedom
## AIC: 1702.8
##
## Number of Fisher Scoring iterations: 4maxTropT_glm <- glm(in_hospital_death ~ TroponinT_max, data=icu_patients_df1, family="binomial")
summary(maxTropT_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ TroponinT_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.0740 -0.5503 -0.5430 -0.5416 1.9965
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.84719 0.06917 -26.705 <2e-16 ***
## TroponinT_max 0.06537 0.02638 2.478 0.0132 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1694.1 on 2059 degrees of freedom
## AIC: 1698.1
##
## Number of Fisher Scoring iterations: 4minUrine_glm <- glm(in_hospital_death ~ Urine_min, data=icu_patients_df1, family="binomial")
summary(minUrine_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ Urine_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6034 -0.5952 -0.5631 -0.5105 2.9438
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.610937 0.076052 -21.182 < 2e-16 ***
## Urine_min -0.006020 0.001787 -3.369 0.000756 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1683.1 on 2059 degrees of freedom
## AIC: 1687.1
##
## Number of Fisher Scoring iterations: 5minWBC_glm <- glm(in_hospital_death ~ WBC_min, data=icu_patients_df1, family="binomial")
summary(minWBC_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ WBC_min, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2861 -0.5638 -0.5477 -0.5315 2.0563
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.987167 0.119356 -16.649 <2e-16 ***
## WBC_min 0.017452 0.008437 2.068 0.0386 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1695.6 on 2059 degrees of freedom
## AIC: 1699.6
##
## Number of Fisher Scoring iterations: 4maxWBC_glm <- glm(in_hospital_death ~ WBC_max, data=icu_patients_df1, family="binomial")
summary(maxWBC_glm) # is significant##
## Call:
## glm(formula = in_hospital_death ~ WBC_max, family = "binomial",
## data = icu_patients_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.2674 -0.5631 -0.5475 -0.5326 2.0545
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.982652 0.118080 -16.791 <2e-16 ***
## WBC_max 0.014086 0.006859 2.054 0.04 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1699.7 on 2060 degrees of freedom
## Residual deviance: 1695.7 on 2059 degrees of freedom
## AIC: 1699.7
##
## Number of Fisher Scoring iterations: 4Univariate Models Findings
- Variables that had a significant Wald test, resulting a rejection of the null hypothesis concluding that the variable is significant in explaining the outcome variable of
in_hospital_deathare:- age
- ICUType
- Weight_max
- Albumin_min
- Bilirubin_max
- BUN_max
- Creatinine_max
- GCS_min
- Glucose_max
- HCO3_min
- HR_max
- Lactate_max
- Na_min
- NISysABP_min
- pH_min
- RespRate_min
- RespRate_max
- Temp_min
- TroponinT_max
- Urine_min
- WBC_min
- WBC_max
- Variables that resulted in a non-significant Wald test are:
Glucose_minHR_minK_minK_maxMAP_minNa_maxNISysABP_maxPlatelets_minPFratiopH_maxTemp_maxTroponinI_max
Multivariable logistic regression models:
## Create a dataset without missing or invalid data to use to build the model ##
## in order to remain consistent and allow comparisons between models to be made ##
# Check counts of missing data in each variable
for(i in 1:length(colnames(icu_patients_df1))){
print(c(i,colnames(icu_patients_df1[i]), sum(is.na(icu_patients_df1[i]))))
}## [1] "1" "RecordID" "0"
## [1] "2" "Length_of_stay" "0"
## [1] "3" "SAPS1" "96"
## [1] "4" "SOFA" "0"
## [1] "5" "Survival" "1288"
## [1] "6" "in_hospital_death" "0"
## [1] "7" "Days" "0"
## [1] "8" "Status" "0"
## [1] "9" "Age" "0"
## [1] "10" "Albumin_diff" "0"
## [1] "11" "Albumin_max" "0"
## [1] "12" "Albumin_min" "0"
## [1] "13" "ALP_diff" "0"
## [1] "14" "ALP_max" "0"
## [1] "15" "ALP_min" "0"
## [1] "16" "ALT_diff" "0"
## [1] "17" "ALT_max" "0"
## [1] "18" "ALT_min" "0"
## [1] "19" "AST_diff" "0"
## [1] "20" "AST_max" "0"
## [1] "21" "AST_min" "0"
## [1] "22" "Bilirubin_diff" "0"
## [1] "23" "Bilirubin_max" "0"
## [1] "24" "Bilirubin_min" "0"
## [1] "25" "BUN_diff" "0"
## [1] "26" "BUN_max" "0"
## [1] "27" "BUN_min" "0"
## [1] "28" "Cholesterol_diff" "0"
## [1] "29" "Cholesterol_max" "0"
## [1] "30" "Cholesterol_min" "0"
## [1] "31" "Creatinine_diff" "0"
## [1] "32" "Creatinine_max" "0"
## [1] "33" "Creatinine_min" "0"
## [1] "34" "DiasABP_diff" "715"
## [1] "35" "DiasABP_max" "715"
## [1] "36" "DiasABP_min" "715"
## [1] "37" "FiO2_diff" "0"
## [1] "38" "FiO2_max" "0"
## [1] "39" "FiO2_min" "0"
## [1] "40" "GCS_diff" "0"
## [1] "41" "GCS_max" "0"
## [1] "42" "GCS_min" "0"
## [1] "43" "Gender" "0"
## [1] "44" "Glucose_diff" "0"
## [1] "45" "Glucose_max" "0"
## [1] "46" "Glucose_min" "0"
## [1] "47" "HCO3_diff" "0"
## [1] "48" "HCO3_max" "0"
## [1] "49" "HCO3_min" "0"
## [1] "50" "HCT_diff" "0"
## [1] "51" "HCT_max" "0"
## [1] "52" "HCT_min" "0"
## [1] "53" "Height" "992"
## [1] "54" "HR_diff" "0"
## [1] "55" "HR_max" "0"
## [1] "56" "HR_min" "0"
## [1] "57" "ICUType" "0"
## [1] "58" "K_diff" "0"
## [1] "59" "K_max" "0"
## [1] "60" "K_min" "0"
## [1] "61" "Lactate_diff" "0"
## [1] "62" "Lactate_max" "0"
## [1] "63" "Lactate_min" "0"
## [1] "64" "MAP_diff" "0"
## [1] "65" "MAP_max" "0"
## [1] "66" "MAP_min" "0"
## [1] "67" "Mg_diff" "0"
## [1] "68" "Mg_max" "0"
## [1] "69" "Mg_min" "0"
## [1] "70" "Na_diff" "0"
## [1] "71" "Na_max" "0"
## [1] "72" "Na_min" "0"
## [1] "73" "NIDiasABP_diff" "455"
## [1] "74" "NIDiasABP_max" "455"
## [1] "75" "NIDiasABP_min" "455"
## [1] "76" "NIMAP_diff" "455"
## [1] "77" "NIMAP_max" "455"
## [1] "78" "NIMAP_min" "455"
## [1] "79" "NISysABP_diff" "453"
## [1] "80" "NISysABP_max" "453"
## [1] "81" "NISysABP_min" "453"
## [1] "82" "PaCO2_diff" "0"
## [1] "83" "PaCO2_max" "0"
## [1] "84" "PaCO2_min" "0"
## [1] "85" "PaO2_diff" "0"
## [1] "86" "PaO2_max" "0"
## [1] "87" "PaO2_min" "0"
## [1] "88" "pH_diff" "0"
## [1] "89" "pH_max" "0"
## [1] "90" "pH_min" "0"
## [1] "91" "Platelets_diff" "0"
## [1] "92" "Platelets_max" "0"
## [1] "93" "Platelets_min" "0"
## [1] "94" "RespRate_diff" "0"
## [1] "95" "RespRate_max" "0"
## [1] "96" "RespRate_min" "0"
## [1] "97" "SaO2_diff" "0"
## [1] "98" "SaO2_max" "0"
## [1] "99" "SaO2_min" "0"
## [1] "100" "SysABP_diff" "715"
## [1] "101" "SysABP_max" "715"
## [1] "102" "SysABP_min" "715"
## [1] "103" "Temp_diff" "0"
## [1] "104" "Temp_max" "0"
## [1] "105" "Temp_min" "0"
## [1] "106" "TroponinI_diff" "0"
## [1] "107" "TroponinI_max" "0"
## [1] "108" "TroponinI_min" "0"
## [1] "109" "TroponinT_diff" "0"
## [1] "110" "TroponinT_max" "0"
## [1] "111" "TroponinT_min" "0"
## [1] "112" "Urine_diff" "0"
## [1] "113" "Urine_max" "0"
## [1] "114" "Urine_min" "0"
## [1] "115" "WBC_diff" "0"
## [1] "116" "WBC_max" "0"
## [1] "117" "WBC_min" "0"
## [1] "118" "Weight_diff" "146"
## [1] "119" "Weight_max" "146"
## [1] "120" "Weight_min" "146"
## [1] "121" "PFratio" "0"## Result: of the variables chosen to explore for the survival model, large amounts of missing data in:
## Height (992), NISysABP_min (453), NISysABP_max (453), Weight_max (146)
## Decision: include Weight_max; remove Height, NISysABP_min, NISysABP_max
# Check counts of negative data (noted some -1 values) in each variable
for(i in 1:length(colnames(icu_patients_df1))){
print(c(i,colnames(icu_patients_df1[i]), sum(icu_patients_df1[i] < 0)))
}## [1] "1" "RecordID" "0"
## [1] "2" "Length_of_stay" "25"
## [1] "3" "SAPS1" NA
## [1] "4" "SOFA" "65"
## [1] "5" "Survival" NA
## [1] "6" "in_hospital_death" "0"
## [1] "7" "Days" "0"
## [1] "8" "Status" "0"
## [1] "9" "Age" "0"
## [1] "10" "Albumin_diff" "0"
## [1] "11" "Albumin_max" "0"
## [1] "12" "Albumin_min" "0"
## [1] "13" "ALP_diff" "0"
## [1] "14" "ALP_max" "0"
## [1] "15" "ALP_min" "0"
## [1] "16" "ALT_diff" "0"
## [1] "17" "ALT_max" "0"
## [1] "18" "ALT_min" "0"
## [1] "19" "AST_diff" "0"
## [1] "20" "AST_max" "0"
## [1] "21" "AST_min" "0"
## [1] "22" "Bilirubin_diff" "0"
## [1] "23" "Bilirubin_max" "0"
## [1] "24" "Bilirubin_min" "0"
## [1] "25" "BUN_diff" "0"
## [1] "26" "BUN_max" "0"
## [1] "27" "BUN_min" "0"
## [1] "28" "Cholesterol_diff" "0"
## [1] "29" "Cholesterol_max" "0"
## [1] "30" "Cholesterol_min" "0"
## [1] "31" "Creatinine_diff" "0"
## [1] "32" "Creatinine_max" "0"
## [1] "33" "Creatinine_min" "0"
## [1] "34" "DiasABP_diff" NA
## [1] "35" "DiasABP_max" NA
## [1] "36" "DiasABP_min" NA
## [1] "37" "FiO2_diff" "0"
## [1] "38" "FiO2_max" "0"
## [1] "39" "FiO2_min" "0"
## [1] "40" "GCS_diff" "0"
## [1] "41" "GCS_max" "0"
## [1] "42" "GCS_min" "0"## Warning in Ops.factor(left, right): '<' not meaningful for factors## [1] "43" "Gender" NA
## [1] "44" "Glucose_diff" "0"
## [1] "45" "Glucose_max" "0"
## [1] "46" "Glucose_min" "0"
## [1] "47" "HCO3_diff" "0"
## [1] "48" "HCO3_max" "0"
## [1] "49" "HCO3_min" "0"
## [1] "50" "HCT_diff" "0"
## [1] "51" "HCT_max" "0"
## [1] "52" "HCT_min" "0"
## [1] "53" "Height" NA
## [1] "54" "HR_diff" "0"
## [1] "55" "HR_max" "0"
## [1] "56" "HR_min" "0"## Warning in Ops.factor(left, right): '<' not meaningful for factors## [1] "57" "ICUType" NA
## [1] "58" "K_diff" "0"
## [1] "59" "K_max" "0"
## [1] "60" "K_min" "0"
## [1] "61" "Lactate_diff" "0"
## [1] "62" "Lactate_max" "0"
## [1] "63" "Lactate_min" "0"
## [1] "64" "MAP_diff" "0"
## [1] "65" "MAP_max" "0"
## [1] "66" "MAP_min" "0"
## [1] "67" "Mg_diff" "0"
## [1] "68" "Mg_max" "0"
## [1] "69" "Mg_min" "0"
## [1] "70" "Na_diff" "0"
## [1] "71" "Na_max" "0"
## [1] "72" "Na_min" "0"
## [1] "73" "NIDiasABP_diff" NA
## [1] "74" "NIDiasABP_max" NA
## [1] "75" "NIDiasABP_min" NA
## [1] "76" "NIMAP_diff" NA
## [1] "77" "NIMAP_max" NA
## [1] "78" "NIMAP_min" NA
## [1] "79" "NISysABP_diff" NA
## [1] "80" "NISysABP_max" NA
## [1] "81" "NISysABP_min" NA
## [1] "82" "PaCO2_diff" "0"
## [1] "83" "PaCO2_max" "0"
## [1] "84" "PaCO2_min" "0"
## [1] "85" "PaO2_diff" "0"
## [1] "86" "PaO2_max" "0"
## [1] "87" "PaO2_min" "0"
## [1] "88" "pH_diff" "0"
## [1] "89" "pH_max" "0"
## [1] "90" "pH_min" "0"
## [1] "91" "Platelets_diff" "0"
## [1] "92" "Platelets_max" "0"
## [1] "93" "Platelets_min" "0"
## [1] "94" "RespRate_diff" "0"
## [1] "95" "RespRate_max" "0"
## [1] "96" "RespRate_min" "0"
## [1] "97" "SaO2_diff" "0"
## [1] "98" "SaO2_max" "0"
## [1] "99" "SaO2_min" "0"
## [1] "100" "SysABP_diff" NA
## [1] "101" "SysABP_max" NA
## [1] "102" "SysABP_min" NA
## [1] "103" "Temp_diff" "0"
## [1] "104" "Temp_max" "0"
## [1] "105" "Temp_min" "0"
## [1] "106" "TroponinI_diff" "0"
## [1] "107" "TroponinI_max" "0"
## [1] "108" "TroponinI_min" "0"
## [1] "109" "TroponinT_diff" "0"
## [1] "110" "TroponinT_max" "0"
## [1] "111" "TroponinT_min" "0"
## [1] "112" "Urine_diff" "0"
## [1] "113" "Urine_max" "0"
## [1] "114" "Urine_min" "0"
## [1] "115" "WBC_diff" "0"
## [1] "116" "WBC_max" "0"
## [1] "117" "WBC_min" "0"
## [1] "118" "Weight_diff" NA
## [1] "119" "Weight_max" NA
## [1] "120" "Weight_min" NA
## [1] "121" "PFratio" "0"## Result: negative values in Length_of_stay and SOFA (not listed in initial choice of variables anyway)
# Create a new dataset with the only non-missing data from list of initial variables chosen
# (excluding those with very high missingness i.e. Height, NISysABP_min, NISysABP_max)
nm_icu_model_df1 <- na.omit(subset(icu_patients_df1,
select=c(Days, Status, # the survival object variables (for task 2)
RecordID, # keep record id for reference if needed
in_hospital_death, # for task 1
Age, Gender, ICUType, Weight_max,
Albumin_min, Bilirubin_max,
BUN_max, Creatinine_max,
GCS_max, Glucose_min, Glucose_max,
HCO3_min, HR_min, HR_max, K_min,
K_max, Lactate_max, MAP_min, Na_min,
Na_max, Platelets_min, PFratio, pH_min,
pH_max, RespRate_min, RespRate_max,
Temp_min, Temp_max, TroponinT_max,
TroponinI_max, Urine_min, WBC_min, WBC_max)))
# all variables from initially selected predictors
full_glm <- glm(in_hospital_death ~
Age +
Gender +
ICUType +
Weight_max +
Albumin_min +
Bilirubin_max +
BUN_max +
Creatinine_max +
GCS_max +
Glucose_min +
Glucose_max +
HCO3_min +
HR_min +
HR_max +
K_min +
K_max +
Lactate_max +
MAP_min +
Na_min +
Na_max +
Platelets_min +
PFratio +
pH_min +
pH_max +
RespRate_min +
RespRate_max +
Temp_min +
Temp_max +
TroponinT_max +
TroponinI_max +
Urine_min +
WBC_min +
WBC_max
,data=nm_icu_model_df1, family="binomial")
summary(full_glm) #AIC 1332.1##
## Call:
## glm(formula = in_hospital_death ~ Age + Gender + ICUType + Weight_max +
## Albumin_min + Bilirubin_max + BUN_max + Creatinine_max +
## GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min +
## HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min +
## Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min +
## RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max +
## Urine_min + WBC_min + WBC_max, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0025 -0.5414 -0.3387 -0.1826 3.1551
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 24.7550693 11.0324370 2.244 0.024842 *
## Age 0.0355727 0.0055679 6.389 1.67e-10 ***
## GenderMale -0.0005774 0.1586626 -0.004 0.997097
## ICUTypeCardiac Surgery Recovery Unit -1.1946684 0.3314631 -3.604 0.000313 ***
## ICUTypeMedical ICU 0.1457551 0.2305142 0.632 0.527188
## ICUTypeSurgical ICU 0.1776610 0.2563794 0.693 0.488334
## Weight_max -0.0041882 0.0037136 -1.128 0.259409
## Albumin_min -0.3103087 0.1269198 -2.445 0.014488 *
## Bilirubin_max 0.0397973 0.0145689 2.732 0.006301 **
## BUN_max 0.0218067 0.0041617 5.240 1.61e-07 ***
## Creatinine_max -0.0512660 0.0566167 -0.905 0.365204
## GCS_max -0.1896782 0.0267396 -7.094 1.31e-12 ***
## Glucose_min 0.0004277 0.0017341 0.247 0.805197
## Glucose_max 0.0005729 0.0010105 0.567 0.570710
## HCO3_min 0.0094985 0.0185570 0.512 0.608753
## HR_min 0.0110264 0.0057790 1.908 0.056391 .
## HR_max 0.0046164 0.0038442 1.201 0.229792
## K_min -0.0801749 0.1621385 -0.494 0.620964
## K_max -0.0707587 0.1016629 -0.696 0.486420
## Lactate_max 0.0645205 0.0365291 1.766 0.077350 .
## MAP_min -0.0001513 0.0044240 -0.034 0.972727
## Na_min 0.0041071 0.0353159 0.116 0.907418
## Na_max -0.0648695 0.0356990 -1.817 0.069198 .
## Platelets_min -0.0009868 0.0008076 -1.222 0.221726
## PFratio -0.0001635 0.0007894 -0.207 0.835900
## pH_min -1.2268398 0.9477985 -1.294 0.195524
## pH_max -0.1918512 1.4140768 -0.136 0.892080
## RespRate_min -0.0231207 0.0254338 -0.909 0.363322
## RespRate_max 0.0138618 0.0122981 1.127 0.259680
## Temp_min -0.1907196 0.0883748 -2.158 0.030922 *
## Temp_max -0.0308143 0.1062282 -0.290 0.771758
## TroponinT_max 0.0188442 0.0354984 0.531 0.595525
## TroponinI_max -0.0028271 0.0078796 -0.359 0.719758
## Urine_min -0.0063152 0.0026190 -2.411 0.015897 *
## WBC_min 0.0656428 0.0277205 2.368 0.017883 *
## WBC_max -0.0521569 0.0229737 -2.270 0.023190 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1260.1 on 1879 degrees of freedom
## AIC: 1332.1
##
## Number of Fisher Scoring iterations: 6###
# variables that were significant on univariate comparisons
signifUni_glm <- glm(in_hospital_death ~
Age +
ICUType +
Weight_max +
Albumin_min +
Bilirubin_max +
BUN_max +
Creatinine_max +
GCS_max +
Glucose_max +
HCO3_min +
HR_max +
Lactate_max +
Na_min +
# NISysABP_min + this was removed from the na.omit part anyway
pH_min +
RespRate_min +
RespRate_max +
Temp_min +
TroponinT_max +
Urine_min +
WBC_min +
WBC_max
,data=nm_icu_model_df1, family="binomial")
summary(signifUni_glm) #AIC 1320.9##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Weight_max +
## Albumin_min + Bilirubin_max + BUN_max + Creatinine_max +
## GCS_max + Glucose_max + HCO3_min + HR_max + Lactate_max +
## Na_min + pH_min + RespRate_min + RespRate_max + Temp_min +
## TroponinT_max + Urine_min + WBC_min + WBC_max, family = "binomial",
## data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9897 -0.5398 -0.3458 -0.1906 3.0306
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.799e+01 6.567e+00 2.739 0.006157 **
## Age 3.404e-02 5.318e-03 6.401 1.55e-10 ***
## ICUTypeCardiac Surgery Recovery Unit -1.087e+00 3.073e-01 -3.538 0.000403 ***
## ICUTypeMedical ICU 1.537e-01 2.259e-01 0.680 0.496226
## ICUTypeSurgical ICU 1.585e-01 2.470e-01 0.642 0.521184
## Weight_max -3.417e-03 3.473e-03 -0.984 0.325245
## Albumin_min -3.454e-01 1.223e-01 -2.824 0.004737 **
## Bilirubin_max 4.376e-02 1.403e-02 3.120 0.001811 **
## BUN_max 2.101e-02 3.916e-03 5.365 8.10e-08 ***
## Creatinine_max -6.020e-02 5.508e-02 -1.093 0.274450
## GCS_max -1.781e-01 2.490e-02 -7.155 8.39e-13 ***
## Glucose_max -6.786e-07 7.610e-04 -0.001 0.999288
## HCO3_min 6.078e-03 1.765e-02 0.344 0.730494
## HR_max 7.162e-03 3.308e-03 2.165 0.030393 *
## Lactate_max 6.304e-02 3.494e-02 1.804 0.071235 .
## Na_min -4.359e-02 1.467e-02 -2.972 0.002959 **
## pH_min -1.172e+00 8.056e-01 -1.455 0.145582
## RespRate_min -1.761e-02 2.465e-02 -0.715 0.474870
## RespRate_max 1.419e-02 1.103e-02 1.287 0.198258
## Temp_min -1.578e-01 7.993e-02 -1.974 0.048379 *
## TroponinT_max 1.198e-02 3.453e-02 0.347 0.728694
## Urine_min -6.348e-03 2.574e-03 -2.467 0.013643 *
## WBC_min 6.828e-02 2.601e-02 2.625 0.008672 **
## WBC_max -6.037e-02 2.207e-02 -2.736 0.006225 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1272.9 on 1891 degrees of freedom
## AIC: 1320.9
##
## Number of Fisher Scoring iterations: 6###
# variables that were significant in the full_glm
signifFull_glm <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
Temp_min +
Urine_min +
WBC_min +
WBC_max
,data=nm_icu_model_df1, family="binomial")
summary(signifFull_glm) #AIC 1330.2##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + Temp_min + Urine_min +
## WBC_min + WBC_max, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8919 -0.5497 -0.3649 -0.2046 3.0349
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 6.356911 2.698679 2.356 0.01849 *
## Age 0.030984 0.004850 6.389 1.67e-10 ***
## ICUTypeCardiac Surgery Recovery Unit -1.206231 0.286775 -4.206 2.60e-05 ***
## ICUTypeMedical ICU 0.065555 0.210415 0.312 0.75538
## ICUTypeSurgical ICU -0.033654 0.229228 -0.147 0.88328
## Albumin_min -0.380485 0.118054 -3.223 0.00127 **
## Bilirubin_max 0.054089 0.013137 4.117 3.83e-05 ***
## BUN_max 0.017585 0.002832 6.209 5.34e-10 ***
## GCS_max -0.179975 0.020954 -8.589 < 2e-16 ***
## Temp_min -0.201811 0.073755 -2.736 0.00621 **
## Urine_min -0.007162 0.002585 -2.770 0.00560 **
## WBC_min 0.055865 0.024568 2.274 0.02297 *
## WBC_max -0.044776 0.020492 -2.185 0.02889 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1304.2 on 1902 degrees of freedom
## AIC: 1330.2
##
## Number of Fisher Scoring iterations: 6# no missing data removed due to missingness
# anova doesn't work because different missing data between the models
anova(full_glm, signifUni_glm, test="Chisq") # the parameters different between the models are not significant## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + Gender + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min +
## Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max +
## Lactate_max + MAP_min + Na_min + Na_max + Platelets_min +
## PFratio + pH_min + pH_max + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min +
## WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min +
## RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min +
## WBC_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1879 1260.1
## 2 1891 1272.9 -12 -12.783 0.385anova(full_glm, signifFull_glm, test="Chisq") # the dropped parameters between the two models do matter## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + Gender + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min +
## Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max +
## Lactate_max + MAP_min + Na_min + Na_max + Platelets_min +
## PFratio + pH_min + pH_max + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min +
## WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + Temp_min + Urine_min + WBC_min + WBC_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1879 1260.1
## 2 1902 1304.2 -23 -44.154 0.005039 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1###
# using the model with the lowest AIC
# reduce it even further
reduced_signifUni_glm <- step(signifUni_glm, trace=1)## Start: AIC=1320.87
## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min +
## RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min +
## WBC_max
##
## Df Deviance AIC
## - Glucose_max 1 1272.9 1318.9
## - HCO3_min 1 1273.0 1319.0
## - TroponinT_max 1 1273.0 1319.0
## - RespRate_min 1 1273.4 1319.4
## - Weight_max 1 1273.9 1319.9
## - Creatinine_max 1 1274.1 1320.1
## - RespRate_max 1 1274.5 1320.5
## <none> 1272.9 1320.9
## - Lactate_max 1 1276.1 1322.1
## - pH_min 1 1276.6 1322.6
## - Temp_min 1 1276.9 1322.9
## - HR_max 1 1277.5 1323.5
## - WBC_min 1 1280.1 1326.1
## - Urine_min 1 1280.9 1326.9
## - WBC_max 1 1280.9 1326.9
## - Albumin_min 1 1280.9 1326.9
## - Na_min 1 1281.6 1327.6
## - Bilirubin_max 1 1282.3 1328.3
## - ICUType 3 1302.5 1344.5
## - BUN_max 1 1302.5 1348.5
## - Age 1 1318.7 1364.7
## - GCS_max 1 1325.1 1371.1
##
## Step: AIC=1318.87
## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HCO3_min +
## HR_max + Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max +
## Temp_min + TroponinT_max + Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## - TroponinT_max 1 1273.0 1317.0
## - HCO3_min 1 1273.0 1317.0
## - RespRate_min 1 1273.4 1317.4
## - Weight_max 1 1273.9 1317.9
## - Creatinine_max 1 1274.1 1318.1
## - RespRate_max 1 1274.5 1318.5
## <none> 1272.9 1318.9
## - Lactate_max 1 1276.2 1320.2
## - pH_min 1 1276.6 1320.6
## - Temp_min 1 1276.9 1320.9
## - HR_max 1 1277.5 1321.5
## - WBC_min 1 1280.1 1324.1
## - Urine_min 1 1280.9 1324.9
## - WBC_max 1 1280.9 1324.9
## - Albumin_min 1 1281.0 1325.0
## - Na_min 1 1281.7 1325.7
## - Bilirubin_max 1 1282.4 1326.4
## - ICUType 3 1303.2 1343.2
## - BUN_max 1 1302.6 1346.6
## - Age 1 1318.8 1362.8
## - GCS_max 1 1325.3 1369.3
##
## Step: AIC=1316.99
## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HCO3_min +
## HR_max + Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max +
## Temp_min + Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## - HCO3_min 1 1273.1 1315.1
## - RespRate_min 1 1273.5 1315.5
## - Weight_max 1 1274.0 1316.0
## - Creatinine_max 1 1274.2 1316.2
## - RespRate_max 1 1274.7 1316.7
## <none> 1273.0 1317.0
## - Lactate_max 1 1276.7 1318.7
## - Temp_min 1 1277.0 1319.0
## - pH_min 1 1277.1 1319.1
## - HR_max 1 1277.5 1319.5
## - WBC_min 1 1280.6 1322.6
## - Urine_min 1 1281.0 1323.0
## - Albumin_min 1 1281.2 1323.2
## - WBC_max 1 1281.4 1323.4
## - Na_min 1 1282.0 1324.0
## - Bilirubin_max 1 1282.9 1324.9
## - ICUType 3 1303.3 1341.3
## - BUN_max 1 1302.7 1344.7
## - Age 1 1318.8 1360.8
## - GCS_max 1 1325.5 1367.5
##
## Step: AIC=1315.11
## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HR_max +
## Lactate_max + Na_min + pH_min + RespRate_min + RespRate_max +
## Temp_min + Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## - RespRate_min 1 1273.6 1313.6
## - Weight_max 1 1274.1 1314.1
## - Creatinine_max 1 1274.4 1314.4
## - RespRate_max 1 1274.8 1314.8
## <none> 1273.1 1315.1
## - Lactate_max 1 1276.7 1316.7
## - Temp_min 1 1277.0 1317.0
## - pH_min 1 1277.1 1317.1
## - HR_max 1 1277.6 1317.6
## - WBC_min 1 1280.9 1320.9
## - Urine_min 1 1281.1 1321.1
## - Albumin_min 1 1281.2 1321.2
## - WBC_max 1 1281.9 1321.9
## - Na_min 1 1282.0 1322.0
## - Bilirubin_max 1 1283.2 1323.2
## - ICUType 3 1303.3 1339.3
## - BUN_max 1 1302.7 1342.7
## - Age 1 1319.3 1359.3
## - GCS_max 1 1325.5 1365.5
##
## Step: AIC=1313.62
## in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + HR_max +
## Lactate_max + Na_min + pH_min + RespRate_max + Temp_min +
## Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## - Weight_max 1 1274.6 1312.6
## - RespRate_max 1 1274.8 1312.8
## - Creatinine_max 1 1274.9 1312.9
## <none> 1273.6 1313.6
## - Lactate_max 1 1277.3 1315.3
## - pH_min 1 1277.4 1315.4
## - Temp_min 1 1277.7 1315.7
## - HR_max 1 1277.9 1315.9
## - Albumin_min 1 1281.5 1319.5
## - Urine_min 1 1281.6 1319.6
## - WBC_min 1 1281.8 1319.8
## - Na_min 1 1282.3 1320.3
## - WBC_max 1 1283.0 1321.0
## - Bilirubin_max 1 1284.3 1322.3
## - ICUType 3 1303.4 1337.4
## - BUN_max 1 1303.3 1341.3
## - Age 1 1319.3 1357.3
## - GCS_max 1 1329.8 1367.8
##
## Step: AIC=1312.62
## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + Creatinine_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + RespRate_max + Temp_min + Urine_min + WBC_min +
## WBC_max
##
## Df Deviance AIC
## - RespRate_max 1 1275.8 1311.8
## - Creatinine_max 1 1276.1 1312.1
## <none> 1274.6 1312.6
## - pH_min 1 1278.2 1314.2
## - Lactate_max 1 1278.3 1314.3
## - HR_max 1 1279.2 1315.2
## - Temp_min 1 1279.5 1315.5
## - Albumin_min 1 1282.3 1318.3
## - Urine_min 1 1282.7 1318.7
## - WBC_min 1 1282.8 1318.8
## - Na_min 1 1283.2 1319.2
## - WBC_max 1 1284.2 1320.2
## - Bilirubin_max 1 1285.2 1321.2
## - ICUType 3 1306.4 1338.4
## - BUN_max 1 1303.7 1339.7
## - Age 1 1326.6 1362.6
## - GCS_max 1 1330.3 1366.3
##
## Step: AIC=1311.85
## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + Creatinine_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## - Creatinine_max 1 1277.1 1311.1
## <none> 1275.8 1311.8
## - Lactate_max 1 1279.5 1313.5
## - pH_min 1 1279.6 1313.6
## - Temp_min 1 1280.3 1314.3
## - HR_max 1 1281.4 1315.4
## - Albumin_min 1 1283.1 1317.1
## - Na_min 1 1283.8 1317.8
## - Urine_min 1 1284.0 1318.0
## - WBC_min 1 1284.0 1318.0
## - WBC_max 1 1285.0 1319.0
## - Bilirubin_max 1 1288.6 1322.6
## - ICUType 3 1307.0 1337.0
## - BUN_max 1 1304.6 1338.6
## - Age 1 1327.0 1361.0
## - GCS_max 1 1342.9 1376.9
##
## Step: AIC=1311.11
## in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
##
## Df Deviance AIC
## <none> 1277.1 1311.1
## - Lactate_max 1 1280.7 1312.7
## - pH_min 1 1280.8 1312.8
## - Temp_min 1 1281.5 1313.5
## - HR_max 1 1282.9 1314.9
## - Na_min 1 1284.5 1316.5
## - Urine_min 1 1284.7 1316.7
## - Albumin_min 1 1284.8 1316.8
## - WBC_min 1 1285.6 1317.6
## - WBC_max 1 1286.6 1318.6
## - Bilirubin_max 1 1289.6 1321.6
## - ICUType 3 1308.6 1336.6
## - BUN_max 1 1314.1 1346.1
## - Age 1 1333.1 1365.1
## - GCS_max 1 1344.1 1376.1# removed variables were:
# Glucose_max
# TroponinT_max
# HCO3_min
# RespRate_min
# Weight_max
# RespRate_max
# Creatinine_max
summary(reduced_signifUni_glm) # AIC 1311.1##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max,
## family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9438 -0.5450 -0.3479 -0.1945 2.9904
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 16.771564 6.180202 2.714 0.00665 **
## Age 0.035748 0.005082 7.034 2.01e-12 ***
## ICUTypeCardiac Surgery Recovery Unit -1.107288 0.292041 -3.792 0.00015 ***
## ICUTypeMedical ICU 0.138003 0.215368 0.641 0.52167
## ICUTypeSurgical ICU 0.123606 0.235752 0.524 0.60007
## Albumin_min -0.330533 0.119828 -2.758 0.00581 **
## Bilirubin_max 0.048073 0.013358 3.599 0.00032 ***
## BUN_max 0.017653 0.002894 6.101 1.06e-09 ***
## GCS_max -0.177828 0.021643 -8.217 < 2e-16 ***
## HR_max 0.007771 0.003215 2.417 0.01564 *
## Lactate_max 0.062615 0.033026 1.896 0.05797 .
## Na_min -0.038723 0.014114 -2.744 0.00608 **
## pH_min -1.101299 0.756621 -1.456 0.14552
## Temp_min -0.162389 0.078329 -2.073 0.03816 *
## Urine_min -0.006031 0.002509 -2.404 0.01622 *
## WBC_min 0.072729 0.025587 2.842 0.00448 **
## WBC_max -0.063857 0.021592 -2.957 0.00310 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1277.1 on 1898 degrees of freedom
## AIC: 1311.1
##
## Number of Fisher Scoring iterations: 6anova(reduced_signifUni_glm,signifUni_glm, test="Chisq") ## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_max + Lactate_max + Na_min + pH_min + RespRate_min +
## RespRate_max + Temp_min + TroponinT_max + Urine_min + WBC_min +
## WBC_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1891 1272.9 7 4.2406 0.7517# p value not significant, the dropped parameters are not significantcommentary to explain developing the models above
Final multivariable logistic regression model:
# same as model above: reduced_signifUni_glm
finalICU_glm <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max
,data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm) # AIC 1311.1##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max,
## family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9438 -0.5450 -0.3479 -0.1945 2.9904
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 16.771564 6.180202 2.714 0.00665 **
## Age 0.035748 0.005082 7.034 2.01e-12 ***
## ICUTypeCardiac Surgery Recovery Unit -1.107288 0.292041 -3.792 0.00015 ***
## ICUTypeMedical ICU 0.138003 0.215368 0.641 0.52167
## ICUTypeSurgical ICU 0.123606 0.235752 0.524 0.60007
## Albumin_min -0.330533 0.119828 -2.758 0.00581 **
## Bilirubin_max 0.048073 0.013358 3.599 0.00032 ***
## BUN_max 0.017653 0.002894 6.101 1.06e-09 ***
## GCS_max -0.177828 0.021643 -8.217 < 2e-16 ***
## HR_max 0.007771 0.003215 2.417 0.01564 *
## Lactate_max 0.062615 0.033026 1.896 0.05797 .
## Na_min -0.038723 0.014114 -2.744 0.00608 **
## pH_min -1.101299 0.756621 -1.456 0.14552
## Temp_min -0.162389 0.078329 -2.073 0.03816 *
## Urine_min -0.006031 0.002509 -2.404 0.01622 *
## WBC_min 0.072729 0.025587 2.842 0.00448 **
## WBC_max -0.063857 0.021592 -2.957 0.00310 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1277.1 on 1898 degrees of freedom
## AIC: 1311.1
##
## Number of Fisher Scoring iterations: 6### testing interactions
# finalICU_glm_AgeCr = finalICU_glm + Age:Creatinine_max
finalICU_glm_AgeCr <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# interaction term
Age:Creatinine_max # creatinine generally increases with age
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_AgeCr) # AIC 1311.6##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:Creatinine_max, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0058 -0.5441 -0.3471 -0.1923 3.0126
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 17.2042718 6.2610209 2.748 0.005999 **
## Age 0.0364778 0.0051215 7.123 1.06e-12 ***
## ICUTypeCardiac Surgery Recovery Unit -1.1050590 0.2924687 -3.778 0.000158 ***
## ICUTypeMedical ICU 0.1432747 0.2157226 0.664 0.506587
## ICUTypeSurgical ICU 0.1270050 0.2361028 0.538 0.590631
## Albumin_min -0.3200195 0.1202310 -2.662 0.007775 **
## Bilirubin_max 0.0482335 0.0133563 3.611 0.000305 ***
## BUN_max 0.0207435 0.0038808 5.345 9.04e-08 ***
## GCS_max -0.1779749 0.0216652 -8.215 < 2e-16 ***
## HR_max 0.0075795 0.0032185 2.355 0.018524 *
## Lactate_max 0.0634961 0.0330932 1.919 0.055022 .
## Na_min -0.0404502 0.0141531 -2.858 0.004263 **
## pH_min -1.1307197 0.7701256 -1.468 0.142042
## Temp_min -0.1627020 0.0784203 -2.075 0.038010 *
## Urine_min -0.0064029 0.0025826 -2.479 0.013166 *
## WBC_min 0.0713769 0.0255692 2.792 0.005246 **
## WBC_max -0.0630659 0.0215458 -2.927 0.003422 **
## Age:Creatinine_max -0.0010441 0.0008793 -1.187 0.235047
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1275.6 on 1897 degrees of freedom
## AIC: 1311.6
##
## Number of Fisher Scoring iterations: 6# finalICU_glm_AgeTemp = finalICU_glm + Age:Temp_min
finalICU_glm_AgeTemp <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# interaction term
Age:Temp_min # low temp more often associated with illness in the elderly e.g. cold sepsis
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_AgeTemp) # AIC 1313.1##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:Temp_min, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9443 -0.5449 -0.3478 -0.1945 2.9890
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 16.295971 11.197145 1.455 0.145567
## Age 0.042771 0.137985 0.310 0.756586
## ICUTypeCardiac Surgery Recovery Unit -1.107832 0.292268 -3.790 0.000150 ***
## ICUTypeMedical ICU 0.137945 0.215393 0.640 0.521891
## ICUTypeSurgical ICU 0.123568 0.235776 0.524 0.600216
## Albumin_min -0.330377 0.119870 -2.756 0.005849 **
## Bilirubin_max 0.048084 0.013358 3.600 0.000319 ***
## BUN_max 0.017650 0.002894 6.098 1.07e-09 ***
## GCS_max -0.177900 0.021689 -8.202 2.36e-16 ***
## HR_max 0.007774 0.003216 2.418 0.015615 *
## Lactate_max 0.062704 0.033071 1.896 0.057949 .
## Na_min -0.038711 0.014117 -2.742 0.006103 **
## pH_min -1.101215 0.756691 -1.455 0.145585
## Temp_min -0.149186 0.270756 -0.551 0.581637
## Urine_min -0.006032 0.002509 -2.404 0.016222 *
## WBC_min 0.072782 0.025611 2.842 0.004486 **
## WBC_max -0.063901 0.021611 -2.957 0.003108 **
## Age:Temp_min -0.000196 0.003848 -0.051 0.959380
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1277.1 on 1897 degrees of freedom
## AIC: 1313.1
##
## Number of Fisher Scoring iterations: 6# finalICU_glm_AgeWeight = finalICU_glm + Age:Weight_max (rather than using Weight_min previously)
finalICU_glm_AgeWeight <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# interaction term
Age:Weight_max # weight generally decreases with age
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_AgeWeight) # AIC 1311##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:Weight_max, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0043 -0.5467 -0.3475 -0.1917 3.0545
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.710e+01 6.323e+00 2.704 0.006847 **
## Age 3.949e-02 5.739e-03 6.882 5.92e-12 ***
## ICUTypeCardiac Surgery Recovery Unit -1.068e+00 2.934e-01 -3.639 0.000273 ***
## ICUTypeMedical ICU 1.308e-01 2.157e-01 0.607 0.544177
## ICUTypeSurgical ICU 1.330e-01 2.361e-01 0.563 0.573176
## Albumin_min -3.363e-01 1.199e-01 -2.805 0.005039 **
## Bilirubin_max 4.833e-02 1.338e-02 3.612 0.000304 ***
## BUN_max 1.823e-02 2.924e-03 6.233 4.57e-10 ***
## GCS_max -1.790e-01 2.169e-02 -8.253 < 2e-16 ***
## HR_max 7.452e-03 3.230e-03 2.307 0.021042 *
## Lactate_max 6.444e-02 3.315e-02 1.944 0.051930 .
## Na_min -3.907e-02 1.409e-02 -2.772 0.005564 **
## pH_min -1.201e+00 7.874e-01 -1.525 0.127242
## Temp_min -1.458e-01 7.896e-02 -1.846 0.064889 .
## Urine_min -5.978e-03 2.507e-03 -2.384 0.017109 *
## WBC_min 7.239e-02 2.559e-02 2.829 0.004674 **
## WBC_max -6.299e-02 2.162e-02 -2.914 0.003568 **
## Age:Weight_max -7.005e-05 5.052e-05 -1.387 0.165553
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1275.1 on 1897 degrees of freedom
## AIC: 1311.1
##
## Number of Fisher Scoring iterations: 6# finalICU_glm_AgeAlbumin = finalICU_glm + Age:Albumin_min
finalICU_glm_AgeAlbumin <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# interaction term
Age:Albumin_min # albumin generally decreases with age
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_AgeAlbumin) # AIC 1309##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:Albumin_min, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9359 -0.5523 -0.3464 -0.1840 3.0218
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 19.347306 6.173815 3.134 0.001726 **
## Age -0.004992 0.021570 -0.231 0.816990
## ICUTypeCardiac Surgery Recovery Unit -1.101538 0.292134 -3.771 0.000163 ***
## ICUTypeMedical ICU 0.125775 0.215780 0.583 0.559971
## ICUTypeSurgical ICU 0.125709 0.235844 0.533 0.594021
## Albumin_min -1.355174 0.548435 -2.471 0.013474 *
## Bilirubin_max 0.048750 0.013410 3.635 0.000278 ***
## BUN_max 0.017767 0.002897 6.133 8.62e-10 ***
## GCS_max -0.177107 0.021686 -8.167 3.16e-16 ***
## HR_max 0.007565 0.003220 2.350 0.018782 *
## Lactate_max 0.062344 0.033194 1.878 0.060356 .
## Na_min -0.037919 0.014226 -2.666 0.007687 **
## pH_min -1.070276 0.727151 -1.472 0.141054
## Temp_min -0.164386 0.078641 -2.090 0.036588 *
## Urine_min -0.005912 0.002509 -2.356 0.018449 *
## WBC_min 0.074097 0.025585 2.896 0.003778 **
## WBC_max -0.063696 0.021561 -2.954 0.003135 **
## Age:Albumin_min 0.014583 0.007592 1.921 0.054741 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1273.4 on 1897 degrees of freedom
## AIC: 1309.4
##
## Number of Fisher Scoring iterations: 6# finalICU_glm_AgeICUType = finalICU_glm + Age:ICUType
finalICU_glm_AgeICUType <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# interaction term
Age:ICUType # age is likely to be related to ICU type
# e.g. elderly more likely to have poor outcome
# after surgery requiring post-op ICU support
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_AgeICUType) # AIC 1307##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:ICUType, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9579 -0.5488 -0.3415 -0.1920 3.1057
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 17.858479 6.317804 2.827 0.004703
## Age 0.028563 0.015297 1.867 0.061863
## ICUTypeCardiac Surgery Recovery Unit -0.137499 1.721588 -0.080 0.936343
## ICUTypeMedical ICU 0.199901 1.243496 0.161 0.872284
## ICUTypeSurgical ICU -2.152542 1.365680 -1.576 0.114987
## Albumin_min -0.327271 0.121006 -2.705 0.006839
## Bilirubin_max 0.047961 0.013482 3.557 0.000374
## BUN_max 0.018057 0.002897 6.232 4.6e-10
## GCS_max -0.179741 0.021736 -8.269 < 2e-16
## HR_max 0.008283 0.003228 2.566 0.010299
## Lactate_max 0.061953 0.033160 1.868 0.061719
## Na_min -0.039643 0.014137 -2.804 0.005043
## pH_min -1.121623 0.768555 -1.459 0.144457
## Temp_min -0.170873 0.079380 -2.153 0.031350
## Urine_min -0.006144 0.002517 -2.441 0.014655
## WBC_min 0.072986 0.025797 2.829 0.004666
## WBC_max -0.065673 0.021802 -3.012 0.002594
## Age:ICUTypeCardiac Surgery Recovery Unit -0.013777 0.023475 -0.587 0.557276
## Age:ICUTypeMedical ICU -0.001538 0.016578 -0.093 0.926097
## Age:ICUTypeSurgical ICU 0.031959 0.018202 1.756 0.079123
##
## (Intercept) **
## Age .
## ICUTypeCardiac Surgery Recovery Unit
## ICUTypeMedical ICU
## ICUTypeSurgical ICU
## Albumin_min **
## Bilirubin_max ***
## BUN_max ***
## GCS_max ***
## HR_max *
## Lactate_max .
## Na_min **
## pH_min
## Temp_min *
## Urine_min *
## WBC_min **
## WBC_max **
## Age:ICUTypeCardiac Surgery Recovery Unit
## Age:ICUTypeMedical ICU
## Age:ICUTypeSurgical ICU .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1266.9 on 1895 degrees of freedom
## AIC: 1306.9
##
## Number of Fisher Scoring iterations: 6# Code from previous attempt at task 1
# Gender:HCT, PaO2:RespRate not tested because they are not in the final model
# Anova testing for the new models
lapply(list(finalICU_glm_AgeCr, finalICU_glm_AgeTemp, finalICU_glm_AgeWeight,
finalICU_glm_AgeAlbumin, finalICU_glm_AgeICUType),
function(x) {print(anova(finalICU_glm, x, test="Chisq"))} )## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Creatinine_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1275.6 1 1.4776 0.2242
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Temp_min
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1277.1 1 0.0025966 0.9594
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Weight_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1275.1 1 1.9802 0.1594
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Albumin_min
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1273.4 1 3.6995 0.05443 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:ICUType
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1895 1266.9 3 10.254 0.01653 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## [[1]]
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Creatinine_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1275.6 1 1.4776 0.2242
##
## [[2]]
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Temp_min
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1277.1 1 0.0025966 0.9594
##
## [[3]]
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Weight_max
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1275.1 1 1.9802 0.1594
##
## [[4]]
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:Albumin_min
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1897 1273.4 1 3.6995 0.05443 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[5]]
## Analysis of Deviance Table
##
## Model 1: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max
## Model 2: in_hospital_death ~ Age + ICUType + Albumin_min + Bilirubin_max +
## BUN_max + GCS_max + HR_max + Lactate_max + Na_min + pH_min +
## Temp_min + Urine_min + WBC_min + WBC_max + Age:ICUType
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 1898 1277.1
## 2 1895 1266.9 3 10.254 0.01653 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Result: borderline effect for age:albumin (p=0.054)
## significant effect for age:icutype (p=0.016)
# Input the significant interactions into the model
finalICU_glm_interactions <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# significant interaction terms
Age:ICUType + Age:Albumin_min
, data=nm_icu_model_df1, family="binomial")
summary(finalICU_glm_interactions) # AIC 1305 (lowest so far - lower than just including age:icutype)##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:ICUType + Age:Albumin_min, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9494 -0.5533 -0.3360 -0.1854 3.2388
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 20.855206 6.365565 3.276 0.00105
## Age -0.018285 0.028752 -0.636 0.52480
## ICUTypeCardiac Surgery Recovery Unit -0.562192 1.733448 -0.324 0.74570
## ICUTypeMedical ICU -0.243286 1.265623 -0.192 0.84756
## ICUTypeSurgical ICU -2.505360 1.374546 -1.823 0.06835
## Albumin_min -1.384342 0.567281 -2.440 0.01467
## Bilirubin_max 0.048779 0.013523 3.607 0.00031
## BUN_max 0.018215 0.002902 6.276 3.47e-10
## GCS_max -0.178502 0.021748 -8.208 2.26e-16
## HR_max 0.008056 0.003232 2.492 0.01269
## Lactate_max 0.062277 0.033295 1.870 0.06142
## Na_min -0.038919 0.014253 -2.731 0.00632
## pH_min -1.084124 0.737653 -1.470 0.14164
## Temp_min -0.172788 0.079499 -2.173 0.02974
## Urine_min -0.006015 0.002511 -2.395 0.01660
## WBC_min 0.074082 0.025771 2.875 0.00405
## WBC_max -0.065411 0.021751 -3.007 0.00264
## Age:ICUTypeCardiac Surgery Recovery Unit -0.008024 0.023597 -0.340 0.73383
## Age:ICUTypeMedical ICU 0.004228 0.016843 0.251 0.80181
## Age:ICUTypeSurgical ICU 0.036583 0.018295 2.000 0.04554
## Age:Albumin_min 0.014994 0.007834 1.914 0.05563
##
## (Intercept) **
## Age
## ICUTypeCardiac Surgery Recovery Unit
## ICUTypeMedical ICU
## ICUTypeSurgical ICU .
## Albumin_min *
## Bilirubin_max ***
## BUN_max ***
## GCS_max ***
## HR_max *
## Lactate_max .
## Na_min **
## pH_min
## Temp_min *
## Urine_min *
## WBC_min **
## WBC_max **
## Age:ICUTypeCardiac Surgery Recovery Unit
## Age:ICUTypeMedical ICU
## Age:ICUTypeSurgical ICU *
## Age:Albumin_min .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1263.2 on 1894 degrees of freedom
## AIC: 1305.2
##
## Number of Fisher Scoring iterations: 6? Do we include this poisson section, or just discuss it? ***
Testing the modified poisson regression, as the outcome is 14% in this data (>10% - common)
#################################################################################
# NEED TO DECIDE WHETHER TO INCLUDE THIS SECTION
# test using modified poisson regression for more common outcomes on the same covariates as above
finalICU_glm_poisson <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max
# changed dataset to fit what we use for rest of task 1
, data=nm_icu_model_df1, family="poisson"(link="log"))
summary(finalICU_glm_poisson) # AIC 1432.5##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max,
## family = poisson(link = "log"), data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6209 -0.5193 -0.3710 -0.2358 2.4255
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 8.073192 3.021690 2.672 0.007546 **
## Age 0.027348 0.004236 6.456 1.07e-10 ***
## ICUTypeCardiac Surgery Recovery Unit -0.931815 0.257304 -3.621 0.000293 ***
## ICUTypeMedical ICU 0.071266 0.178517 0.399 0.689738
## ICUTypeSurgical ICU 0.069801 0.196761 0.355 0.722775
## Albumin_min -0.254955 0.097939 -2.603 0.009236 **
## Bilirubin_max 0.030818 0.008837 3.487 0.000488 ***
## BUN_max 0.010432 0.001960 5.324 1.02e-07 ***
## GCS_max -0.121144 0.016972 -7.138 9.47e-13 ***
## HR_max 0.005007 0.002452 2.042 0.041161 *
## Lactate_max 0.026759 0.020284 1.319 0.187094
## Na_min -0.029362 0.011261 -2.607 0.009122 **
## pH_min -0.367651 0.221104 -1.663 0.096353 .
## Temp_min -0.103899 0.050598 -2.053 0.040031 *
## Urine_min -0.004947 0.002199 -2.249 0.024500 *
## WBC_min 0.045769 0.020587 2.223 0.026203 *
## WBC_max -0.039644 0.017408 -2.277 0.022765 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1082.2 on 1914 degrees of freedom
## Residual deviance: 832.5 on 1898 degrees of freedom
## AIC: 1432.5
##
## Number of Fisher Scoring iterations: 6# fewer significant variables (likely as CI can be wider in poisson)
# but the variables that are significant were also significant in the logistic model
# examine ORs from logistic regression
options(scipen=999) # turn off scientific notation
exp(coef(finalICU_glm_interactions))## (Intercept)
## 1141039705.79856825
## Age
## 0.98188117
## ICUTypeCardiac Surgery Recovery Unit
## 0.56995835
## ICUTypeMedical ICU
## 0.78404694
## ICUTypeSurgical ICU
## 0.08164616
## Albumin_min
## 0.25048853
## Bilirubin_max
## 1.04998791
## BUN_max
## 1.01838146
## GCS_max
## 0.83652254
## HR_max
## 1.00808840
## Lactate_max
## 1.06425731
## Na_min
## 0.96182843
## pH_min
## 0.33819783
## Temp_min
## 0.84131613
## Urine_min
## 0.99400267
## WBC_min
## 1.07689505
## WBC_max
## 0.93668260
## Age:ICUTypeCardiac Surgery Recovery Unit
## 0.99200823
## Age:ICUTypeMedical ICU
## 1.00423652
## Age:ICUTypeSurgical ICU
## 1.03725988
## Age:Albumin_min
## 1.01510738# examine RRs from logistic regression
exp(coef(finalICU_glm_poisson))## (Intercept) Age
## 3207.3233507 1.0277252
## ICUTypeCardiac Surgery Recovery Unit ICUTypeMedical ICU
## 0.3938384 1.0738665
## ICUTypeSurgical ICU Albumin_min
## 1.0722952 0.7749514
## Bilirubin_max BUN_max
## 1.0312976 1.0104869
## GCS_max HR_max
## 0.8859060 1.0050193
## Lactate_max Na_min
## 1.0271202 0.9710651
## pH_min Temp_min
## 0.6923591 0.9013161
## Urine_min WBC_min
## 0.9950657 1.0468326
## WBC_max
## 0.9611318# the ORs and RRs appear very similar --> check the actual differences
exp(coef(finalICU_glm_interactions))-exp(coef(finalICU_glm_poisson))## Warning in exp(coef(finalICU_glm_interactions)) -
## exp(coef(finalICU_glm_poisson)): longer object length is not a multiple of
## shorter object length## (Intercept)
## 1141036498.475217581
## Age
## -0.045844015
## ICUTypeCardiac Surgery Recovery Unit
## 0.176119966
## ICUTypeMedical ICU
## -0.289819588
## ICUTypeSurgical ICU
## -0.990649004
## Albumin_min
## -0.524462846
## Bilirubin_max
## 0.018690293
## BUN_max
## 0.007894516
## GCS_max
## -0.049383432
## HR_max
## 0.003069046
## Lactate_max
## 0.037137079
## Na_min
## -0.009236685
## pH_min
## -0.354161276
## Temp_min
## -0.059999922
## Urine_min
## -0.001063029
## WBC_min
## 0.030062482
## WBC_max
## -0.024449219
## Age:ICUTypeCardiac Surgery Recovery Unit
## -3206.331342461
## Age:ICUTypeMedical ICU
## -0.023488663
## Age:ICUTypeSurgical ICU
## 0.643421501
## Age:Albumin_min
## -0.058759150# the intercept is very different (by 1141036498?!) - not sure how to interpret that. the other estimates are very similar
# perhaps the logistic model is therefore justified? just need to be careful in interpretation using 'odds' rather than 'risk'
#################################################################################Final model diagnostics:
### Goodness of fit using bins df1 ###
# add predicted probabilities to the data frame
nm_icu_model_df1 %>% mutate(predprob=predict(finalICU_glm_interactions, type="response"),
linpred=predict(finalICU_glm_interactions)) %>%
# group the data into bins based on the linear predictor fitted values
group_by(cut(linpred, breaks=unique(quantile(linpred, (1:50)/51)))) %>%
# summarise by bin
summarise(death_bin=sum(in_hospital_death), predprob_bin=mean(predprob), n_bin=n()) %>%
# add the standard error of the mean predicted probaility for each bin
mutate(se_predprob_bin=sqrt(predprob_bin*(1 - predprob_bin)/n_bin)) %>%
# plot it with 95% confidence interval bars
ggplot(aes(x=predprob_bin,
y=death_bin/n_bin,
ymin=death_bin/n_bin - 1.96*se_predprob_bin,
ymax=death_bin/n_bin + 1.96*se_predprob_bin)) +
geom_point() + geom_linerange(colour="orange", alpha=0.4) +
geom_abline(intercept=0, slope=1) +
labs(x="Predicted probability (binned)",
y="Observed proportion (in each bin)")
# the ideal calibration line fits within most of the dots and their 95% CI
### Goodness of fit using Hosmer Lemeshow stat ###
nm_icu_model_df1 %>% mutate(predprob=predict(finalICU_glm_interactions, type="response"),
linpred=predict(finalICU_glm_interactions)) %>%
group_by(cut(linpred, breaks=unique(quantile(linpred, (1:50)/51)))) %>%
summarise(death_bin=sum(in_hospital_death), predprob_bin=mean(predprob), n_bin=n()) %>%
mutate(se_predprob_bin=sqrt(predprob_bin*(1 - predprob_bin)/n_bin)) -> hl_df
hl_stat <- with(hl_df, sum( (death_bin - n_bin*predprob_bin)^2 /
(n_bin* predprob_bin*(1 - predprob_bin))))
hl <- c(hosmer_lemeshow_stat=hl_stat, hl_degrees_freedom=nrow(hl_df) - 1)
hl## hosmer_lemeshow_stat hl_degrees_freedom
## 51.77871 49.00000# calculate p-value
c(p_val=1 - pchisq(hl[1], hl[2])) # the p value here is not statistically significant, indicating no lack of fit## p_val.hosmer_lemeshow_stat
## 0.3659299### Brier score ###
get_brier <- function(model){
predprob <- predict(model, type="response")
Brier_score <- mean((predprob - nm_icu_model_df1$in_hospital_death)^2)
return(Brier_score)
}
get_brier(finalICU_glm)## [1] 0.1022154get_brier(finalICU_glm_interactions)## [1] 0.1012639# the final model with interactions has slightly lower brier score -> lower score is better fitRe-fitting the model to the original data:
#### re-fit your final model to the unimputed data frame
# (`icu_patients_df0.rds`) and comment on any differences you find
# compared to the same model fitted to the data without imputation,
df0_finalICU_glm_interactions <- glm(in_hospital_death ~
Age +
ICUType +
Albumin_min +
Bilirubin_max +
BUN_max +
GCS_max +
HR_max +
Lactate_max +
Na_min +
pH_min +
Temp_min +
Urine_min +
WBC_min +
WBC_max +
# significant interaction terms
Age:ICUType + Age:Albumin_min
, data=icu_patients_df0, family="binomial")
summary(df0_finalICU_glm_interactions) ##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:ICUType + Age:Albumin_min, family = "binomial", data = icu_patients_df0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.0796 -0.5851 -0.3221 -0.1132 3.0310
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 27.261971 15.618682 1.745 0.080903
## Age 0.084514 0.074238 1.138 0.254949
## ICUTypeCardiac Surgery Recovery Unit 0.730898 5.521035 0.132 0.894680
## ICUTypeMedical ICU -0.147974 3.093787 -0.048 0.961852
## ICUTypeSurgical ICU 0.681712 3.226486 0.211 0.832664
## Albumin_min -0.111573 1.334217 -0.084 0.933355
## Bilirubin_max 0.045677 0.031016 1.473 0.140834
## BUN_max 0.022170 0.006091 3.640 0.000273
## GCS_max -0.149812 0.050123 -2.989 0.002800
## HR_max 0.014980 0.008350 1.794 0.072819
## Lactate_max 0.050180 0.068215 0.736 0.461960
## Na_min -0.065969 0.039336 -1.677 0.093532
## pH_min -1.749588 1.905015 -0.918 0.358403
## Temp_min -0.279081 0.158228 -1.764 0.077767
## Urine_min -0.002243 0.005209 -0.431 0.666708
## WBC_min 0.108851 0.053332 2.041 0.041250
## WBC_max -0.107694 0.042883 -2.511 0.012027
## Age:ICUTypeCardiac Surgery Recovery Unit -0.054997 0.083252 -0.661 0.508866
## Age:ICUTypeMedical ICU -0.002158 0.044497 -0.049 0.961315
## Age:ICUTypeSurgical ICU -0.022395 0.046757 -0.479 0.631968
## Age:Albumin_min -0.012685 0.019718 -0.643 0.520011
##
## (Intercept) .
## Age
## ICUTypeCardiac Surgery Recovery Unit
## ICUTypeMedical ICU
## ICUTypeSurgical ICU
## Albumin_min
## Bilirubin_max
## BUN_max ***
## GCS_max **
## HR_max .
## Lactate_max
## Na_min .
## pH_min
## Temp_min .
## Urine_min
## WBC_min *
## WBC_max *
## Age:ICUTypeCardiac Surgery Recovery Unit
## Age:ICUTypeMedical ICU
## Age:ICUTypeSurgical ICU
## Age:Albumin_min
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 307.90 on 298 degrees of freedom
## Residual deviance: 215.99 on 278 degrees of freedom
## (1762 observations deleted due to missingness)
## AIC: 257.99
##
## Number of Fisher Scoring iterations: 6# when using the predictors from our final df1 model with interactions onto df0 data
# 1762 observations of data is removed due to missingness
# the AIC is very low 253 - less data = easier to predict?
summary(finalICU_glm)##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max,
## family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9438 -0.5450 -0.3479 -0.1945 2.9904
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) 16.771564 6.180202 2.714
## Age 0.035748 0.005082 7.034
## ICUTypeCardiac Surgery Recovery Unit -1.107288 0.292041 -3.792
## ICUTypeMedical ICU 0.138003 0.215368 0.641
## ICUTypeSurgical ICU 0.123606 0.235752 0.524
## Albumin_min -0.330533 0.119828 -2.758
## Bilirubin_max 0.048073 0.013358 3.599
## BUN_max 0.017653 0.002894 6.101
## GCS_max -0.177828 0.021643 -8.217
## HR_max 0.007771 0.003215 2.417
## Lactate_max 0.062615 0.033026 1.896
## Na_min -0.038723 0.014114 -2.744
## pH_min -1.101299 0.756621 -1.456
## Temp_min -0.162389 0.078329 -2.073
## Urine_min -0.006031 0.002509 -2.404
## WBC_min 0.072729 0.025587 2.842
## WBC_max -0.063857 0.021592 -2.957
## Pr(>|z|)
## (Intercept) 0.00665 **
## Age 0.00000000000201 ***
## ICUTypeCardiac Surgery Recovery Unit 0.00015 ***
## ICUTypeMedical ICU 0.52167
## ICUTypeSurgical ICU 0.60007
## Albumin_min 0.00581 **
## Bilirubin_max 0.00032 ***
## BUN_max 0.00000000105685 ***
## GCS_max < 0.0000000000000002 ***
## HR_max 0.01564 *
## Lactate_max 0.05797 .
## Na_min 0.00608 **
## pH_min 0.14552
## Temp_min 0.03816 *
## Urine_min 0.01622 *
## WBC_min 0.00448 **
## WBC_max 0.00310 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1277.1 on 1898 degrees of freedom
## AIC: 1311.1
##
## Number of Fisher Scoring iterations: 6summary(finalICU_glm_interactions)##
## Call:
## glm(formula = in_hospital_death ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HR_max + Lactate_max +
## Na_min + pH_min + Temp_min + Urine_min + WBC_min + WBC_max +
## Age:ICUType + Age:Albumin_min, family = "binomial", data = nm_icu_model_df1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9494 -0.5533 -0.3360 -0.1854 3.2388
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) 20.855206 6.365565 3.276
## Age -0.018285 0.028752 -0.636
## ICUTypeCardiac Surgery Recovery Unit -0.562192 1.733448 -0.324
## ICUTypeMedical ICU -0.243286 1.265623 -0.192
## ICUTypeSurgical ICU -2.505360 1.374546 -1.823
## Albumin_min -1.384342 0.567281 -2.440
## Bilirubin_max 0.048779 0.013523 3.607
## BUN_max 0.018215 0.002902 6.276
## GCS_max -0.178502 0.021748 -8.208
## HR_max 0.008056 0.003232 2.492
## Lactate_max 0.062277 0.033295 1.870
## Na_min -0.038919 0.014253 -2.731
## pH_min -1.084124 0.737653 -1.470
## Temp_min -0.172788 0.079499 -2.173
## Urine_min -0.006015 0.002511 -2.395
## WBC_min 0.074082 0.025771 2.875
## WBC_max -0.065411 0.021751 -3.007
## Age:ICUTypeCardiac Surgery Recovery Unit -0.008024 0.023597 -0.340
## Age:ICUTypeMedical ICU 0.004228 0.016843 0.251
## Age:ICUTypeSurgical ICU 0.036583 0.018295 2.000
## Age:Albumin_min 0.014994 0.007834 1.914
## Pr(>|z|)
## (Intercept) 0.00105 **
## Age 0.52480
## ICUTypeCardiac Surgery Recovery Unit 0.74570
## ICUTypeMedical ICU 0.84756
## ICUTypeSurgical ICU 0.06835 .
## Albumin_min 0.01467 *
## Bilirubin_max 0.00031 ***
## BUN_max 0.000000000347023992 ***
## GCS_max 0.000000000000000226 ***
## HR_max 0.01269 *
## Lactate_max 0.06142 .
## Na_min 0.00632 **
## pH_min 0.14164
## Temp_min 0.02974 *
## Urine_min 0.01660 *
## WBC_min 0.00405 **
## WBC_max 0.00264 **
## Age:ICUTypeCardiac Surgery Recovery Unit 0.73383
## Age:ICUTypeMedical ICU 0.80181
## Age:ICUTypeSurgical ICU 0.04554 *
## Age:Albumin_min 0.05563 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1604.2 on 1914 degrees of freedom
## Residual deviance: 1263.2 on 1894 degrees of freedom
## AIC: 1305.2
##
## Number of Fisher Scoring iterations: 6# variables significant in finalICU_glm
# Age
# ICUTypeCardiac Surgery Recovery unit
# Albumin_min
# Bilirubin_max
# BUN_max
# GCS_max
# HR_max
# Na_min
# Temp_min
# Urine_min
# WBC_min
# WBC_max
# variables significant in finalICU_glm_interactions
# Albumin_min
# Bilirubin_max
# BUN_max
# GCS_max
# HR_max
# Na_min
# Temp_min
# Urine_min
# WBC_min
# WBC_max
# Age:ICUTypeSurgicalICU
# variables significant in df0_finalICU_glm_interactions
# BUN_max
# GCS_max
# WBC_min
# WBC_max
# many of the variables that were significant in the imputed data model, are not significant when fitted to the df0 unimputated data
# more missing variables = less power to produce a statistically significant resultFinal paragraph - summarising the most important findings of your final model & diagnostics. Include the most important values from the statistical output, and a simple clinical interpretation. - ?explain why not poisson - explain what we see when fitting to df0 ***
Task 2 (15 marks)
In this task, you are required to develop a Cox proportional hazards survival model using the icu_patients_df1 data set which adequately explains or predicts the length of survival indicated by the Days variable, with censoring as indicated by the Status variable. You should fit a series of models, maybe three or four, evaluating each one, before you present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge. Aim for between five and ten predictor variables (slightly more or fewer is OK). It is perfectly acceptable to include predictor variables in your final model which are not statistically significant, as long as you justify their inclusion on medical or physiological grounds (you will not be marked down if your medical justification is not exactly correct, but do you best). You should assess each model you consider for goodness of fit and other relevant statistics, and you should assess your final model for violations of assumptions and perform other diagnostics which you think are relevant (and modify the model if indicated, or at least comment on the possible impact of what your diagnostics show). Finally, re-fit your final model to the unimputed data frame (icu_patients_df0.rds) and comment on any differences you find.
Hints
Select an initial subset of explanatory variables that you will use to predict survival. Justify your choice.
Conduct basic exploratory data analysis on your variables of choice.
Fit appropriate univariate Cox proportional hazards models.
Fit an appropriate series of multivariable Cox proportional hazards models, justifying your approach. Assess each model you consider for goodness of fit and other relevant statistics.
Present your final model. Your final model should not include all the predictor variables, just a small subset of them, which you have selected based on statistical significance and/or background knowledge.
For your final model, present a set of diagnostic statistics and/or charts and comment on them.
Write a very brief paragraph summarising the most important findings of your final model. Include the most important values from the statistical output, and a simple clinical interpretation.
Task 2 Response:
Select an initial subset of explanatory variables:
The purpose of this task is to understand the impact of information collected during the first 24 hours of an ICU stay on the length of survival of the ICU population (followed up for 2408 days, approximately 6.5 years).
To select an initial subset of explanatory variables, we used the same clinical logic as for Task 1 - to examine the measures used in already validated risk scores: SAPS1, SOFA and APACHE scores.
Therefore, the initial subset of explanatory variables we have chosen for this task are:
DEMOGRAPHIC VARIABLES:
* Age
* Gender
* ICUType
* Height
* Weight_max
CLINICAL VARIABLES:
* Albumin_min
* Bilirubin_max
* BUN_max
* Creatinine_max
* GCS_min
* Glucose_min and Glucose_max
* HCO3_min
* HR_min and HR_max
* K_min and K_max
* Lactate_max
* MAP_min
* Na_min and Na_max
* NISysABP_min and NISysABP_max
* Platelets_min
* FiO2_max and PaO2_min - included as PFratio= PaO2_min/ FiO2_max
* pH_min and pH_max
* RespRate_min and RespRate_max
* Temp_min and Temp_max
* TroponinI_max
* TroponinT_max
* Urine_min
* WBC_min and WBC_max
Basic initial exploratory data analysis (EDA) and non-parametric survival curves:
# Outcome variables
unique_icu = unique(subset(icu_patients_df1, select = c(RecordID)))
dim(unique_icu) # There are 2061 unique individuals## [1] 2061 1table(icu_patients_df1$Status) #773 censored out of 2061 observations##
## FALSE TRUE
## 1288 773# Plot KM survival curve (non-parametric)
ICU.fit <- survfit( Surv(Days, Status) ~ 1, data = icu_patients_df1)
print(ICU.fit, print.rmean = TRUE)## Call: survfit(formula = Surv(Days, Status) ~ 1, data = icu_patients_df1)
##
## n events *rmean *se(rmean) median 0.95LCL 0.95UCL
## 2061.0 773.0 1633.5 23.1 NA NA NA
## * restricted mean with upper limit = 2408#summary(ICU.fit)
plot(ICU.fit, main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')
# plotting Nelson-Aalen estimate (non-parametric)
plot(ICU.fit, fun="cumhaz", main = "Nelson-Aalen estimate of cumulative hazard function", xlab = 'Length of survival (in days)')
There were 773 deaths (out of 2061 participants) during follow-up.The median follow-up time cannot be determined as the survival rate has not yet dropped to 50% survival at the end of the available data. The cumulative hazard rate (as shown in the Nelson Aalen plot) reaches 47% by the end of the available data.
# Display frequencies for categorical explanatory variables
table(icu_patients_df1$Gender)##
## Female Male
## 913 1148table(icu_patients_df1$ICUType)##
## Coronary Care Unit Cardiac Surgery Recovery Unit
## 297 448
## Medical ICU Surgical ICU
## 788 528# Display counts, histograms, median and IQRs for continuous explanatory variables
# Create PFratio variable:
icu_patients_df1$PFratio<-icu_patients_df1$PaO2_min/icu_patients_df1$FiO2_max
# Write a function for continuous variable EDA output
cont_eda <- function(variable){
print(paste(variable,'EDA:'))
na_rm <- na.omit(icu_patients_df1[,variable])
print(paste('Number of non-missing values:',length(na_rm))) # number of non-missing values
print(paste('Number of missing values:',sum(is.na(icu_patients_df1[,variable])))) # number of missing values
print(quantile(icu_patients_df1[,variable], na.rm=TRUE))
hist(icu_patients_df1[,variable], breaks=20, xlab=variable, main=paste('Histogram of',variable))
}
# Loop through the continuous variables from the chosen list of variables to explore and pass them to the EDA function
cont_vars <- c('Age', 'Height', 'Weight_max', 'Albumin_min', 'Bilirubin_max',
'BUN_max', 'Creatinine_max', 'GCS_min', 'Glucose_min',
'Glucose_max', 'HCO3_min', 'HR_min', 'HR_max', 'K_min', 'K_max',
'Lactate_max', 'MAP_min', 'Na_min', 'Na_max', 'NISysABP_min',
'NISysABP_max', 'Platelets_min', 'PFratio', 'pH_min', 'pH_max',
'RespRate_min', 'RespRate_max', 'Temp_min', 'Temp_max',
'TroponinI_max', 'TroponinT_max', 'Urine_min', 'WBC_min', 'WBC_max')
par(mfrow=c(12,3)) # set the layout of the histograms in 12 row x 3 column grid
for(i in 1:length(cont_vars)){
cont_eda(cont_vars[i])
}## [1] "Age EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 16 52 67 78 90## [1] "Height EDA:"
## [1] "Number of non-missing values: 1069"
## [1] "Number of missing values: 992"
## 0% 25% 50% 75% 100%
## 13.0 162.6 170.2 177.8 426.7## [1] "Weight_max EDA:"
## [1] "Number of non-missing values: 1915"
## [1] "Number of missing values: 146"
## 0% 25% 50% 75% 100%
## 34.60 66.00 80.00 94.55 230.00## [1] "Albumin_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 1.1 2.6 3.0 3.5 5.3## [1] "Bilirubin_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.1 0.4 0.7 1.3 45.9## [1] "BUN_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 3 14 20 33 197## [1] "Creatinine_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.2 0.8 1.0 1.5 22.0## [1] "GCS_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 3 3 8 14 15## [1] "Glucose_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 24 98 117 141 632## [1] "Glucose_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 39 117 141 180 1143## [1] "HCO3_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 5 20 23 25 44## [1] "HR_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0 61 71 81 126## [1] "HR_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 44 91 104 119 300## [1] "K_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 1.8 3.5 3.9 4.3 6.9## [1] "K_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 2.5 4.0 4.3 4.7 22.9## [1] "Lactate_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.4 1.5 2.2 3.2 29.3## [1] "MAP_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 1 55 61 70 265## [1] "Na_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 98 136 138 141 160## [1] "Na_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 112 137 140 142 177## [1] "NISysABP_min EDA:"
## [1] "Number of non-missing values: 1608"
## [1] "Number of missing values: 453"
## 0% 25% 50% 75% 100%
## 4 83 95 108 234## [1] "NISysABP_max EDA:"
## [1] "Number of non-missing values: 1608"
## [1] "Number of missing values: 453"
## 0% 25% 50% 75% 100%
## 78 121 138 156 274## [1] "Platelets_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 9 126 184 246 891## [1] "PFratio EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 24 85 122 188 1150## [1] "pH_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 3.00 7.28 7.34 7.39 7.63## [1] "pH_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 7.15 7.38 7.42 7.46 7.69## [1] "RespRate_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 4 12 14 17 24## [1] "RespRate_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 13 24 27 33 98## [1] "Temp_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 24.2 35.6 36.1 36.6 38.3## [1] "Temp_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 35.4 37.1 37.6 38.2 42.1## [1] "TroponinI_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.3 2.6 7.8 17.6 43.4## [1] "TroponinT_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.01 0.06 0.17 0.80 24.46## [1] "Urine_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0 0 20 36 600## [1] "WBC_min EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.1 7.6 10.4 14.1 128.3## [1] "WBC_max EDA:"
## [1] "Number of non-missing values: 2061"
## [1] "Number of missing values: 0"
## 0% 25% 50% 75% 100%
## 0.1 9.3 12.3 16.9 155.6
EDA Findings:
There are 2061 unique individuals in the dataset. Of these, 913 are female (44%) and 1148 are male (56%).
Medical ICU accounted for 38% of individuals, 26% in Surgical ICU, 24% in Cardiac Surgery recovery Unit and 14% in the Coronary Care unit.
The following variables have a large proportion of missing observations:
Weight_max- 146 missing observationsHeight- 992 missing observationsNISysABP_min&NISysABP_max- 453 missing observations
The median values (50% quantile) and IQR (25% - 75% quantiles) are displayed for all continuous variables.
Deleted the commentary for median values - I think it is clear from the code output and doesn’t need additional explaining. ***
#Plot the Kaplan-Meier survival curves by categorical variables in the data
#Gender
ICU.gender.fit <- survfit( Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
print(ICU.gender.fit, print.rmean = TRUE)## Call: survfit(formula = Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
##
## n events *rmean *se(rmean) median 0.95LCL 0.95UCL
## as.factor(Gender)=Female 913 364 1588 35.2 NA NA NA
## as.factor(Gender)=Male 1148 409 1670 30.6 NA NA NA
## * restricted mean with upper limit = 2408plot(ICU.gender.fit, col=c("blue", "red"), main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')
legend("bottomleft", legend=c("Female", "Male"),col=c("blue","red"), lty=1:1,cex=1)
#ICUType
ICU.type.fit <- survfit( Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
print(ICU.type.fit, print.rmean = TRUE)## Call: survfit(formula = Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
##
## n events *rmean *se(rmean)
## as.factor(ICUType)=Coronary Care Unit 297 132 1486 63.1
## as.factor(ICUType)=Cardiac Surgery Recovery Unit 448 99 2002 38.9
## as.factor(ICUType)=Medical ICU 788 372 1414 39.3
## as.factor(ICUType)=Surgical ICU 528 170 1731 44.3
## median 0.95LCL 0.95UCL
## as.factor(ICUType)=Coronary Care Unit NA NA NA
## as.factor(ICUType)=Cardiac Surgery Recovery Unit NA NA NA
## as.factor(ICUType)=Medical ICU NA 2051 NA
## as.factor(ICUType)=Surgical ICU NA NA NA
## * restricted mean with upper limit = 2408plot(ICU.type.fit, col=c("blue", "red","purple","green"), main = 'Kaplan-Meier estimate of survival function', xlab = 'Length of survival (in days)')
legend("bottomleft", legend=c("Coronary Care Unit", "Cardiac Surgery Recovery Unit", "Medical ICU", "Surgical ICU"),col=c("blue","red","purple","green"), lty=1:1,cex=1)
The survival curves above show that risk of mortality is greater for the ICU population that is female than those that are male. Furthermore, ICU population mortality by ICU Type is different - those in Medical ICU have the highest risk of mortality whereas those in Cardiac Surgery Recovery Unit have the lowest. Interestingly, the survival curves look parallel for each category indicating Cox proportional hazards model is an appropriate model for ICU related survival.
Univariate Cox proportional hazards models:
# Cox proportional models and Log Rank tests for the chosen variables
# Survival object = Surv(Days, Status)
# Gender
ICU.fitbyGender <- coxph( Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
summary(ICU.fitbyGender)## Call:
## coxph(formula = Surv(Days, Status) ~ as.factor(Gender), data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## as.factor(Gender)Male -0.13708 0.87190 0.07206 -1.902 0.0571 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## as.factor(Gender)Male 0.8719 1.147 0.7571 1.004
##
## Concordance= 0.516 (se = 0.009 )
## Likelihood ratio test= 3.61 on 1 df, p=0.06
## Wald test = 3.62 on 1 df, p=0.06
## Score (logrank) test = 3.62 on 1 df, p=0.06# ICU Type
ICU.fitbytype <- coxph( Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
summary(ICU.fitbytype)## Call:
## coxph(formula = Surv(Days, Status) ~ as.factor(ICUType), data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef)
## as.factor(ICUType)Cardiac Surgery Recovery Unit -0.87895 0.41522 0.13301
## as.factor(ICUType)Medical ICU 0.09362 1.09815 0.10131
## as.factor(ICUType)Surgical ICU -0.39843 0.67137 0.11603
## z Pr(>|z|)
## as.factor(ICUType)Cardiac Surgery Recovery Unit -6.608 0.0000000000389 ***
## as.factor(ICUType)Medical ICU 0.924 0.355437
## as.factor(ICUType)Surgical ICU -3.434 0.000595 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95
## as.factor(ICUType)Cardiac Surgery Recovery Unit 0.4152 2.4084 0.3199
## as.factor(ICUType)Medical ICU 1.0981 0.9106 0.9004
## as.factor(ICUType)Surgical ICU 0.6714 1.4895 0.5348
## upper .95
## as.factor(ICUType)Cardiac Surgery Recovery Unit 0.5389
## as.factor(ICUType)Medical ICU 1.3394
## as.factor(ICUType)Surgical ICU 0.8428
##
## Concordance= 0.597 (se = 0.009 )
## Likelihood ratio test= 98.74 on 3 df, p=<0.0000000000000002
## Wald test = 87.96 on 3 df, p=<0.0000000000000002
## Score (logrank) test = 93.02 on 3 df, p=<0.0000000000000002# Age
ICU.fitbyage <- coxph( Surv(Days, Status) ~ Age, data = icu_patients_df1)
summary(ICU.fitbyage)## Call:
## coxph(formula = Surv(Days, Status) ~ Age, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Age 0.03355 1.03412 0.00250 13.42 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.034 0.967 1.029 1.039
##
## Concordance= 0.646 (se = 0.01 )
## Likelihood ratio test= 209.4 on 1 df, p=<0.0000000000000002
## Wald test = 180.1 on 1 df, p=<0.0000000000000002
## Score (logrank) test = 187 on 1 df, p=<0.0000000000000002# Height
ICU.fitbyheight <- coxph( Surv(Days, Status) ~ Height, data = icu_patients_df1)
summary(ICU.fitbyheight)## Call:
## coxph(formula = Surv(Days, Status) ~ Height, data = icu_patients_df1)
##
## n= 1069, number of events= 385
## (992 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Height -0.003851 0.996156 0.002346 -1.642 0.101
##
## exp(coef) exp(-coef) lower .95 upper .95
## Height 0.9962 1.004 0.9916 1.001
##
## Concordance= 0.541 (se = 0.015 )
## Likelihood ratio test= 2.7 on 1 df, p=0.1
## Wald test = 2.69 on 1 df, p=0.1
## Score (logrank) test = 2.52 on 1 df, p=0.1# Weight_max
ICU.fitbyweightmax <- coxph( Surv(Days, Status) ~ Weight_max, data = icu_patients_df1)
summary(ICU.fitbyweightmax)## Call:
## coxph(formula = Surv(Days, Status) ~ Weight_max, data = icu_patients_df1)
##
## n= 1915, number of events= 721
## (146 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Weight_max -0.007213 0.992813 0.001759 -4.101 0.0000411 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Weight_max 0.9928 1.007 0.9894 0.9962
##
## Concordance= 0.56 (se = 0.011 )
## Likelihood ratio test= 17.9 on 1 df, p=0.00002
## Wald test = 16.82 on 1 df, p=0.00004
## Score (logrank) test = 16.71 on 1 df, p=0.00004# Albumin_min
ICU.fitbyAlbuminmin <- coxph( Surv(Days, Status) ~ Albumin_min, data = icu_patients_df1)
summary(ICU.fitbyAlbuminmin)## Call:
## coxph(formula = Surv(Days, Status) ~ Albumin_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Albumin_min -0.22075 0.80192 0.05704 -3.87 0.000109 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Albumin_min 0.8019 1.247 0.7171 0.8968
##
## Concordance= 0.54 (se = 0.011 )
## Likelihood ratio test= 15.02 on 1 df, p=0.0001
## Wald test = 14.98 on 1 df, p=0.0001
## Score (logrank) test = 14.99 on 1 df, p=0.0001# Bilirubin_max
ICU.fitbyBilirubinmax <- coxph( Surv(Days, Status) ~ Bilirubin_max, data = icu_patients_df1)
summary(ICU.fitbyBilirubinmax)## Call:
## coxph(formula = Surv(Days, Status) ~ Bilirubin_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Bilirubin_max 0.025159 1.025478 0.007431 3.386 0.00071 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Bilirubin_max 1.025 0.9752 1.011 1.041
##
## Concordance= 0.515 (se = 0.011 )
## Likelihood ratio test= 9.48 on 1 df, p=0.002
## Wald test = 11.46 on 1 df, p=0.0007
## Score (logrank) test = 11.7 on 1 df, p=0.0006# BUN_max
ICU.fitbyBUNmax <- coxph( Surv(Days, Status) ~ BUN_max, data = icu_patients_df1)
summary(ICU.fitbyBUNmax)## Call:
## coxph(formula = Surv(Days, Status) ~ BUN_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## BUN_max 0.015002 1.015115 0.001064 14.09 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## BUN_max 1.015 0.9851 1.013 1.017
##
## Concordance= 0.647 (se = 0.01 )
## Likelihood ratio test= 142.5 on 1 df, p=<0.0000000000000002
## Wald test = 198.6 on 1 df, p=<0.0000000000000002
## Score (logrank) test = 207 on 1 df, p=<0.0000000000000002# Creatinine_max
ICU.fitbyCreatininemax <- coxph( Surv(Days, Status) ~ Creatinine_max, data = icu_patients_df1)
summary(ICU.fitbyCreatininemax)## Call:
## coxph(formula = Surv(Days, Status) ~ Creatinine_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Creatinine_max 0.10152 1.10685 0.01467 6.92 0.0000000000045 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Creatinine_max 1.107 0.9035 1.075 1.139
##
## Concordance= 0.594 (se = 0.011 )
## Likelihood ratio test= 35.11 on 1 df, p=0.000000003
## Wald test = 47.89 on 1 df, p=0.000000000005
## Score (logrank) test = 48.54 on 1 df, p=0.000000000003# GCS_min
ICU.fitbyGCSmin <- coxph( Surv(Days, Status) ~ GCS_min, data = icu_patients_df1)
summary(ICU.fitbyGCSmin)## Call:
## coxph(formula = Surv(Days, Status) ~ GCS_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## GCS_min 0.006052 1.006070 0.007324 0.826 0.409
##
## exp(coef) exp(-coef) lower .95 upper .95
## GCS_min 1.006 0.994 0.9917 1.021
##
## Concordance= 0.501 (se = 0.01 )
## Likelihood ratio test= 0.68 on 1 df, p=0.4
## Wald test = 0.68 on 1 df, p=0.4
## Score (logrank) test = 0.68 on 1 df, p=0.4# Glucose - min & max
ICU.fitbyGlucosemin <- coxph( Surv(Days, Status) ~ Glucose_min, data = icu_patients_df1)
summary(ICU.fitbyGlucosemin)## Call:
## coxph(formula = Surv(Days, Status) ~ Glucose_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Glucose_min 0.0014076 1.0014086 0.0007477 1.883 0.0597 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Glucose_min 1.001 0.9986 0.9999 1.003
##
## Concordance= 0.508 (se = 0.011 )
## Likelihood ratio test= 3.31 on 1 df, p=0.07
## Wald test = 3.54 on 1 df, p=0.06
## Score (logrank) test = 3.53 on 1 df, p=0.06ICU.fitbyGlucosemax <- coxph( Surv(Days, Status) ~ Glucose_max, data = icu_patients_df1)
summary(ICU.fitbyGlucosemax)## Call:
## coxph(formula = Surv(Days, Status) ~ Glucose_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Glucose_max 0.0012981 1.0012989 0.0003245 4 0.0000634 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Glucose_max 1.001 0.9987 1.001 1.002
##
## Concordance= 0.547 (se = 0.011 )
## Likelihood ratio test= 13.2 on 1 df, p=0.0003
## Wald test = 16 on 1 df, p=0.00006
## Score (logrank) test = 15.96 on 1 df, p=0.00006# HCO3_min
ICU.fitbyHCO3min <- coxph( Surv(Days, Status) ~ HCO3_min, data = icu_patients_df1)
summary(ICU.fitbyHCO3min)## Call:
## coxph(formula = Surv(Days, Status) ~ HCO3_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## HCO3_min -0.017036 0.983108 0.008023 -2.123 0.0337 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## HCO3_min 0.9831 1.017 0.9678 0.9987
##
## Concordance= 0.535 (se = 0.011 )
## Likelihood ratio test= 4.49 on 1 df, p=0.03
## Wald test = 4.51 on 1 df, p=0.03
## Score (logrank) test = 4.5 on 1 df, p=0.03# HR - min & max
ICU.fitbyHRmin <- coxph( Surv(Days, Status) ~ HR_min, data = icu_patients_df1)
summary(ICU.fitbyHRmin)## Call:
## coxph(formula = Surv(Days, Status) ~ HR_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## HR_min -0.0009841 0.9990164 0.0024165 -0.407 0.684
##
## exp(coef) exp(-coef) lower .95 upper .95
## HR_min 0.999 1.001 0.9943 1.004
##
## Concordance= 0.498 (se = 0.011 )
## Likelihood ratio test= 0.17 on 1 df, p=0.7
## Wald test = 0.17 on 1 df, p=0.7
## Score (logrank) test = 0.17 on 1 df, p=0.7ICU.fitbyHRmax <- coxph( Surv(Days, Status) ~ HR_max, data = icu_patients_df1)
summary(ICU.fitbyHRmax)## Call:
## coxph(formula = Surv(Days, Status) ~ HR_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## HR_max 0.002779 1.002783 0.001648 1.687 0.0916 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## HR_max 1.003 0.9972 0.9996 1.006
##
## Concordance= 0.515 (se = 0.011 )
## Likelihood ratio test= 2.79 on 1 df, p=0.09
## Wald test = 2.85 on 1 df, p=0.09
## Score (logrank) test = 2.84 on 1 df, p=0.09# K - min & max
ICU.fitbyKmin <- coxph( Surv(Days, Status) ~ K_min, data = icu_patients_df1)
summary(ICU.fitbyKmin)## Call:
## coxph(formula = Surv(Days, Status) ~ K_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## K_min 0.03906 1.03983 0.06125 0.638 0.524
##
## exp(coef) exp(-coef) lower .95 upper .95
## K_min 1.04 0.9617 0.9222 1.172
##
## Concordance= 0.502 (se = 0.011 )
## Likelihood ratio test= 0.41 on 1 df, p=0.5
## Wald test = 0.41 on 1 df, p=0.5
## Score (logrank) test = 0.41 on 1 df, p=0.5ICU.fitbyKmax <- coxph( Surv(Days, Status) ~ K_max, data = icu_patients_df1)
summary(ICU.fitbyKmax)## Call:
## coxph(formula = Surv(Days, Status) ~ K_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## K_max 0.07306 1.07579 0.02958 2.469 0.0135 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## K_max 1.076 0.9295 1.015 1.14
##
## Concordance= 0.527 (se = 0.011 )
## Likelihood ratio test= 4.81 on 1 df, p=0.03
## Wald test = 6.1 on 1 df, p=0.01
## Score (logrank) test = 5.98 on 1 df, p=0.01# Lactate_max
ICU.fitbyLactatemax <- coxph( Surv(Days, Status) ~ Lactate_max, data = icu_patients_df1)
summary(ICU.fitbyLactatemax)## Call:
## coxph(formula = Surv(Days, Status) ~ Lactate_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Lactate_max 0.05778 1.05948 0.01666 3.467 0.000526 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Lactate_max 1.059 0.9439 1.025 1.095
##
## Concordance= 0.508 (se = 0.011 )
## Likelihood ratio test= 10.95 on 1 df, p=0.0009
## Wald test = 12.02 on 1 df, p=0.0005
## Score (logrank) test = 12.03 on 1 df, p=0.0005# MAP_min
ICU.fitbyMAPmin <- coxph( Surv(Days, Status) ~ MAP_min, data = icu_patients_df1)
summary(ICU.fitbyMAPmin)## Call:
## coxph(formula = Surv(Days, Status) ~ MAP_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## MAP_min -0.004744 0.995267 0.002326 -2.04 0.0414 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## MAP_min 0.9953 1.005 0.9907 0.9998
##
## Concordance= 0.52 (se = 0.01 )
## Likelihood ratio test= 4.37 on 1 df, p=0.04
## Wald test = 4.16 on 1 df, p=0.04
## Score (logrank) test = 4.07 on 1 df, p=0.04# Na - min & max
ICU.fitbyNamin <- coxph( Surv(Days, Status) ~ Na_min, data = icu_patients_df1)
summary(ICU.fitbyNamin)## Call:
## coxph(formula = Surv(Days, Status) ~ Na_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Na_min -0.021187 0.979036 0.007371 -2.875 0.00405 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Na_min 0.979 1.021 0.965 0.9933
##
## Concordance= 0.536 (se = 0.011 )
## Likelihood ratio test= 7.74 on 1 df, p=0.005
## Wald test = 8.26 on 1 df, p=0.004
## Score (logrank) test = 8.16 on 1 df, p=0.004ICU.fitbyNamax <- coxph( Surv(Days, Status) ~ Na_max, data = icu_patients_df1)
summary(ICU.fitbyNamax)## Call:
## coxph(formula = Surv(Days, Status) ~ Na_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Na_max -0.015698 0.984424 0.008287 -1.894 0.0582 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Na_max 0.9844 1.016 0.9686 1.001
##
## Concordance= 0.521 (se = 0.011 )
## Likelihood ratio test= 3.61 on 1 df, p=0.06
## Wald test = 3.59 on 1 df, p=0.06
## Score (logrank) test = 3.57 on 1 df, p=0.06# NISysABP - min & max
ICU.fitbyNISysABPmin <- coxph( Surv(Days, Status) ~ NISysABP_min, data = icu_patients_df1)
summary(ICU.fitbyNISysABPmin)## Call:
## coxph(formula = Surv(Days, Status) ~ NISysABP_min, data = icu_patients_df1)
##
## n= 1608, number of events= 651
## (453 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## NISysABP_min -0.007374 0.992653 0.001994 -3.699 0.000216 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## NISysABP_min 0.9927 1.007 0.9888 0.9965
##
## Concordance= 0.555 (se = 0.012 )
## Likelihood ratio test= 14 on 1 df, p=0.0002
## Wald test = 13.68 on 1 df, p=0.0002
## Score (logrank) test = 13.54 on 1 df, p=0.0002ICU.fitbyNISysABPmax <- coxph( Surv(Days, Status) ~ NISysABP_max, data = icu_patients_df1)
summary(ICU.fitbyNISysABPmax)## Call:
## coxph(formula = Surv(Days, Status) ~ NISysABP_max, data = icu_patients_df1)
##
## n= 1608, number of events= 651
## (453 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## NISysABP_max 0.003503 1.003509 0.001402 2.498 0.0125 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## NISysABP_max 1.004 0.9965 1.001 1.006
##
## Concordance= 0.523 (se = 0.012 )
## Likelihood ratio test= 6.12 on 1 df, p=0.01
## Wald test = 6.24 on 1 df, p=0.01
## Score (logrank) test = 6.24 on 1 df, p=0.01# Platelets_min
ICU.fitbyPlateletsmin <- coxph( Surv(Days, Status) ~ Platelets_min, data = icu_patients_df1)
summary(ICU.fitbyPlateletsmin)## Call:
## coxph(formula = Surv(Days, Status) ~ Platelets_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Platelets_min 0.0001735 1.0001735 0.0003440 0.504 0.614
##
## exp(coef) exp(-coef) lower .95 upper .95
## Platelets_min 1 0.9998 0.9995 1.001
##
## Concordance= 0.499 (se = 0.011 )
## Likelihood ratio test= 0.25 on 1 df, p=0.6
## Wald test = 0.25 on 1 df, p=0.6
## Score (logrank) test = 0.25 on 1 df, p=0.6# PFratio (PaO2_min/FiO2_max)
ICU.fitbyPFratio <- coxph( Surv(Days, Status) ~ PFratio, data = icu_patients_df1)
summary(ICU.fitbyPFratio)## Call:
## coxph(formula = Surv(Days, Status) ~ PFratio, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## PFratio -0.0002469 0.9997531 0.0003579 -0.69 0.49
##
## exp(coef) exp(-coef) lower .95 upper .95
## PFratio 0.9998 1 0.9991 1
##
## Concordance= 0.513 (se = 0.011 )
## Likelihood ratio test= 0.49 on 1 df, p=0.5
## Wald test = 0.48 on 1 df, p=0.5
## Score (logrank) test = 0.48 on 1 df, p=0.5# pH - min & max
ICU.fitbypHmin <- coxph( Surv(Days, Status) ~ pH_min, data = icu_patients_df1)
summary(ICU.fitbypHmin)## Call:
## coxph(formula = Surv(Days, Status) ~ pH_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## pH_min -0.6668 0.5133 0.1717 -3.884 0.000103 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## pH_min 0.5133 1.948 0.3667 0.7187
##
## Concordance= 0.51 (se = 0.011 )
## Likelihood ratio test= 8.34 on 1 df, p=0.004
## Wald test = 15.09 on 1 df, p=0.0001
## Score (logrank) test = 14.09 on 1 df, p=0.0002ICU.fitbypHmax <- coxph( Surv(Days, Status) ~ pH_max, data = icu_patients_df1)
summary(ICU.fitbypHmax)## Call:
## coxph(formula = Surv(Days, Status) ~ pH_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## pH_max -1.3288 0.2648 0.5512 -2.411 0.0159 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## pH_max 0.2648 3.776 0.0899 0.78
##
## Concordance= 0.524 (se = 0.011 )
## Likelihood ratio test= 5.78 on 1 df, p=0.02
## Wald test = 5.81 on 1 df, p=0.02
## Score (logrank) test = 5.81 on 1 df, p=0.02# RespRate - min & max
ICU.fitbyRespRatemin <- coxph( Surv(Days, Status) ~ RespRate_min, data = icu_patients_df1)
summary(ICU.fitbyRespRatemin)## Call:
## coxph(formula = Surv(Days, Status) ~ RespRate_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## RespRate_min 0.042945 1.043880 0.009451 4.544 0.00000552 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## RespRate_min 1.044 0.958 1.025 1.063
##
## Concordance= 0.555 (se = 0.01 )
## Likelihood ratio test= 20.44 on 1 df, p=0.000006
## Wald test = 20.65 on 1 df, p=0.000006
## Score (logrank) test = 20.67 on 1 df, p=0.000005ICU.fitbyRespRatemax <- coxph( Surv(Days, Status) ~ RespRate_max, data = icu_patients_df1)
summary(ICU.fitbyRespRatemax)## Call:
## coxph(formula = Surv(Days, Status) ~ RespRate_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## RespRate_max 0.01472 1.01483 0.00432 3.407 0.000657 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## RespRate_max 1.015 0.9854 1.006 1.023
##
## Concordance= 0.535 (se = 0.011 )
## Likelihood ratio test= 10.93 on 1 df, p=0.0009
## Wald test = 11.61 on 1 df, p=0.0007
## Score (logrank) test = 11.54 on 1 df, p=0.0007# Temp - min & max
ICU.fitbyTempmin <- coxph( Surv(Days, Status) ~ Temp_min, data = icu_patients_df1)
summary(ICU.fitbyTempmin)## Call:
## coxph(formula = Surv(Days, Status) ~ Temp_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Temp_min -0.10541 0.89996 0.03894 -2.707 0.00679 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Temp_min 0.9 1.111 0.8338 0.9713
##
## Concordance= 0.528 (se = 0.011 )
## Likelihood ratio test= 6.85 on 1 df, p=0.009
## Wald test = 7.33 on 1 df, p=0.007
## Score (logrank) test = 7.21 on 1 df, p=0.007ICU.fitbyTempmax <- coxph( Surv(Days, Status) ~ Temp_max, data = icu_patients_df1)
summary(ICU.fitbyTempmax)## Call:
## coxph(formula = Surv(Days, Status) ~ Temp_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Temp_max -0.1966 0.8215 0.0493 -3.988 0.0000668 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Temp_max 0.8215 1.217 0.7459 0.9049
##
## Concordance= 0.55 (se = 0.011 )
## Likelihood ratio test= 16.34 on 1 df, p=0.00005
## Wald test = 15.9 on 1 df, p=0.00007
## Score (logrank) test = 15.89 on 1 df, p=0.00007# Troponin_max (I and T assays)
ICU.fitbyTroponinImax <- coxph( Surv(Days, Status) ~ TroponinI_max, data = icu_patients_df1)
summary(ICU.fitbyTroponinImax)## Call:
## coxph(formula = Surv(Days, Status) ~ TroponinI_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## TroponinI_max -0.00000905 0.99999095 0.00324098 -0.003 0.998
##
## exp(coef) exp(-coef) lower .95 upper .95
## TroponinI_max 1 1 0.9937 1.006
##
## Concordance= 0.508 (se = 0.011 )
## Likelihood ratio test= 0 on 1 df, p=1
## Wald test = 0 on 1 df, p=1
## Score (logrank) test = 0 on 1 df, p=1ICU.fitbyTroponinTmax <- coxph( Surv(Days, Status) ~ TroponinT_max, data = icu_patients_df1)
summary(ICU.fitbyTroponinTmax)## Call:
## coxph(formula = Surv(Days, Status) ~ TroponinT_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## TroponinT_max 0.04152 1.04239 0.01583 2.623 0.00871 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## TroponinT_max 1.042 0.9593 1.011 1.075
##
## Concordance= 0.525 (se = 0.01 )
## Likelihood ratio test= 6 on 1 df, p=0.01
## Wald test = 6.88 on 1 df, p=0.009
## Score (logrank) test = 6.89 on 1 df, p=0.009# Urine_min
ICU.fitbyUrinemin <- coxph( Surv(Days, Status) ~ Urine_min, data = icu_patients_df1)
summary(ICU.fitbyUrinemin)## Call:
## coxph(formula = Surv(Days, Status) ~ Urine_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## Urine_min -0.0019252 0.9980767 0.0007179 -2.682 0.00733 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Urine_min 0.9981 1.002 0.9967 0.9995
##
## Concordance= 0.525 (se = 0.01 )
## Likelihood ratio test= 8.51 on 1 df, p=0.004
## Wald test = 7.19 on 1 df, p=0.007
## Score (logrank) test = 7.23 on 1 df, p=0.007# WBC - min & max
ICU.fitbyWBCmin <- coxph( Surv(Days, Status) ~ WBC_min, data = icu_patients_df1)
summary(ICU.fitbyWBCmin)## Call:
## coxph(formula = Surv(Days, Status) ~ WBC_min, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## WBC_min 0.009102 1.009144 0.004755 1.914 0.0556 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## WBC_min 1.009 0.9909 0.9998 1.019
##
## Concordance= 0.501 (se = 0.011 )
## Likelihood ratio test= 3.18 on 1 df, p=0.07
## Wald test = 3.66 on 1 df, p=0.06
## Score (logrank) test = 3.59 on 1 df, p=0.06ICU.fitbyWBCmax <- coxph( Surv(Days, Status) ~ WBC_max, data = icu_patients_df1)
summary(ICU.fitbyWBCmax)## Call:
## coxph(formula = Surv(Days, Status) ~ WBC_max, data = icu_patients_df1)
##
## n= 2061, number of events= 773
##
## coef exp(coef) se(coef) z Pr(>|z|)
## WBC_max 0.003928 1.003936 0.004294 0.915 0.36
##
## exp(coef) exp(-coef) lower .95 upper .95
## WBC_max 1.004 0.9961 0.9955 1.012
##
## Concordance= 0.491 (se = 0.011 )
## Likelihood ratio test= 0.79 on 1 df, p=0.4
## Wald test = 0.84 on 1 df, p=0.4
## Score (logrank) test = 0.83 on 1 df, p=0.4Univariable Cox model interpretation by Variable:
Gender- non-significant log-rank test (p-value = 0.06), means that the null hypothesis of no difference in survival between genders is not rejected with a conclusion that survival does not significantly differ by gender.ICUType- significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by each ICU Type. Note that, hazard rate for those in Medical ICU is not statistically significantly different for those in Coronary Care Unit.Age- significant log-rank test (p-value close to 0), means that the null hypothesis is rejected with a conclusion that survival significantly differs by individual’s age. For every year older in age, the risk of mortality increases by approximately 3%.Height- non-significant log-rank test (p-value = 0.1), means that the null hypothesis of no difference in survival for varying heights is not rejected with a conclusion that survival does not significantly differ by height.Weight_max- significant log-rank test (p-value = 0.00004) indicating that the null hypothesis is rejected with a conclusion that survival significantly differs by weight. For every additional kilogram, the risk of mortality reduces by approximately 1%. The use of a centered variable may make it easier to interpret.Clinical measures where the log-rank test results in a rejection of the null hypothesis (p-value <0.05) arguing for the variables’ significance in predicting survival times are:
Albumin_minBilirubin_maxCreatinineBUN_maxCreatinine_maxGlucose_maxHCO3_minK_maxLactate_maxMAP_minNa_minNISysABP_min&NISysABP_maxpH_min&pH_maxRespRate_min&RespRate_maxTemp_min&Temp_maxTroponinT_maxUrine_min
Multivariable Cox proportional hazards models:
## As in Task 1, create a dataset without missing or invalid data to use to build the model ##
## in order to remain consistent and allow comparisons between models to be made ##
# Check counts of missing data in each variable
for(i in 1:length(colnames(icu_patients_df1))){
print(c(i,colnames(icu_patients_df1[i]), sum(is.na(icu_patients_df1[i]))))
}## [1] "1" "RecordID" "0"
## [1] "2" "Length_of_stay" "0"
## [1] "3" "SAPS1" "96"
## [1] "4" "SOFA" "0"
## [1] "5" "Survival" "1288"
## [1] "6" "in_hospital_death" "0"
## [1] "7" "Days" "0"
## [1] "8" "Status" "0"
## [1] "9" "Age" "0"
## [1] "10" "Albumin_diff" "0"
## [1] "11" "Albumin_max" "0"
## [1] "12" "Albumin_min" "0"
## [1] "13" "ALP_diff" "0"
## [1] "14" "ALP_max" "0"
## [1] "15" "ALP_min" "0"
## [1] "16" "ALT_diff" "0"
## [1] "17" "ALT_max" "0"
## [1] "18" "ALT_min" "0"
## [1] "19" "AST_diff" "0"
## [1] "20" "AST_max" "0"
## [1] "21" "AST_min" "0"
## [1] "22" "Bilirubin_diff" "0"
## [1] "23" "Bilirubin_max" "0"
## [1] "24" "Bilirubin_min" "0"
## [1] "25" "BUN_diff" "0"
## [1] "26" "BUN_max" "0"
## [1] "27" "BUN_min" "0"
## [1] "28" "Cholesterol_diff" "0"
## [1] "29" "Cholesterol_max" "0"
## [1] "30" "Cholesterol_min" "0"
## [1] "31" "Creatinine_diff" "0"
## [1] "32" "Creatinine_max" "0"
## [1] "33" "Creatinine_min" "0"
## [1] "34" "DiasABP_diff" "715"
## [1] "35" "DiasABP_max" "715"
## [1] "36" "DiasABP_min" "715"
## [1] "37" "FiO2_diff" "0"
## [1] "38" "FiO2_max" "0"
## [1] "39" "FiO2_min" "0"
## [1] "40" "GCS_diff" "0"
## [1] "41" "GCS_max" "0"
## [1] "42" "GCS_min" "0"
## [1] "43" "Gender" "0"
## [1] "44" "Glucose_diff" "0"
## [1] "45" "Glucose_max" "0"
## [1] "46" "Glucose_min" "0"
## [1] "47" "HCO3_diff" "0"
## [1] "48" "HCO3_max" "0"
## [1] "49" "HCO3_min" "0"
## [1] "50" "HCT_diff" "0"
## [1] "51" "HCT_max" "0"
## [1] "52" "HCT_min" "0"
## [1] "53" "Height" "992"
## [1] "54" "HR_diff" "0"
## [1] "55" "HR_max" "0"
## [1] "56" "HR_min" "0"
## [1] "57" "ICUType" "0"
## [1] "58" "K_diff" "0"
## [1] "59" "K_max" "0"
## [1] "60" "K_min" "0"
## [1] "61" "Lactate_diff" "0"
## [1] "62" "Lactate_max" "0"
## [1] "63" "Lactate_min" "0"
## [1] "64" "MAP_diff" "0"
## [1] "65" "MAP_max" "0"
## [1] "66" "MAP_min" "0"
## [1] "67" "Mg_diff" "0"
## [1] "68" "Mg_max" "0"
## [1] "69" "Mg_min" "0"
## [1] "70" "Na_diff" "0"
## [1] "71" "Na_max" "0"
## [1] "72" "Na_min" "0"
## [1] "73" "NIDiasABP_diff" "455"
## [1] "74" "NIDiasABP_max" "455"
## [1] "75" "NIDiasABP_min" "455"
## [1] "76" "NIMAP_diff" "455"
## [1] "77" "NIMAP_max" "455"
## [1] "78" "NIMAP_min" "455"
## [1] "79" "NISysABP_diff" "453"
## [1] "80" "NISysABP_max" "453"
## [1] "81" "NISysABP_min" "453"
## [1] "82" "PaCO2_diff" "0"
## [1] "83" "PaCO2_max" "0"
## [1] "84" "PaCO2_min" "0"
## [1] "85" "PaO2_diff" "0"
## [1] "86" "PaO2_max" "0"
## [1] "87" "PaO2_min" "0"
## [1] "88" "pH_diff" "0"
## [1] "89" "pH_max" "0"
## [1] "90" "pH_min" "0"
## [1] "91" "Platelets_diff" "0"
## [1] "92" "Platelets_max" "0"
## [1] "93" "Platelets_min" "0"
## [1] "94" "RespRate_diff" "0"
## [1] "95" "RespRate_max" "0"
## [1] "96" "RespRate_min" "0"
## [1] "97" "SaO2_diff" "0"
## [1] "98" "SaO2_max" "0"
## [1] "99" "SaO2_min" "0"
## [1] "100" "SysABP_diff" "715"
## [1] "101" "SysABP_max" "715"
## [1] "102" "SysABP_min" "715"
## [1] "103" "Temp_diff" "0"
## [1] "104" "Temp_max" "0"
## [1] "105" "Temp_min" "0"
## [1] "106" "TroponinI_diff" "0"
## [1] "107" "TroponinI_max" "0"
## [1] "108" "TroponinI_min" "0"
## [1] "109" "TroponinT_diff" "0"
## [1] "110" "TroponinT_max" "0"
## [1] "111" "TroponinT_min" "0"
## [1] "112" "Urine_diff" "0"
## [1] "113" "Urine_max" "0"
## [1] "114" "Urine_min" "0"
## [1] "115" "WBC_diff" "0"
## [1] "116" "WBC_max" "0"
## [1] "117" "WBC_min" "0"
## [1] "118" "Weight_diff" "146"
## [1] "119" "Weight_max" "146"
## [1] "120" "Weight_min" "146"
## [1] "121" "PFratio" "0" ## Result: of the variables chosen to explore for the survival model, large amounts of missing data in:
## Height (992), NISysABP_min (453), NISysABP_max (453), Weight_max (146)
## Decision: include Weight_max; remove Height, NISysABP_min, NISysABP_max
# Check counts of negative data (noted some -1 values) in each variable
for(i in 1:length(colnames(icu_patients_df1))){
print(c(i,colnames(icu_patients_df1[i]), sum(icu_patients_df1[i] < 0)))
}## [1] "1" "RecordID" "0"
## [1] "2" "Length_of_stay" "25"
## [1] "3" "SAPS1" NA
## [1] "4" "SOFA" "65"
## [1] "5" "Survival" NA
## [1] "6" "in_hospital_death" "0"
## [1] "7" "Days" "0"
## [1] "8" "Status" "0"
## [1] "9" "Age" "0"
## [1] "10" "Albumin_diff" "0"
## [1] "11" "Albumin_max" "0"
## [1] "12" "Albumin_min" "0"
## [1] "13" "ALP_diff" "0"
## [1] "14" "ALP_max" "0"
## [1] "15" "ALP_min" "0"
## [1] "16" "ALT_diff" "0"
## [1] "17" "ALT_max" "0"
## [1] "18" "ALT_min" "0"
## [1] "19" "AST_diff" "0"
## [1] "20" "AST_max" "0"
## [1] "21" "AST_min" "0"
## [1] "22" "Bilirubin_diff" "0"
## [1] "23" "Bilirubin_max" "0"
## [1] "24" "Bilirubin_min" "0"
## [1] "25" "BUN_diff" "0"
## [1] "26" "BUN_max" "0"
## [1] "27" "BUN_min" "0"
## [1] "28" "Cholesterol_diff" "0"
## [1] "29" "Cholesterol_max" "0"
## [1] "30" "Cholesterol_min" "0"
## [1] "31" "Creatinine_diff" "0"
## [1] "32" "Creatinine_max" "0"
## [1] "33" "Creatinine_min" "0"
## [1] "34" "DiasABP_diff" NA
## [1] "35" "DiasABP_max" NA
## [1] "36" "DiasABP_min" NA
## [1] "37" "FiO2_diff" "0"
## [1] "38" "FiO2_max" "0"
## [1] "39" "FiO2_min" "0"
## [1] "40" "GCS_diff" "0"
## [1] "41" "GCS_max" "0"
## [1] "42" "GCS_min" "0"## Warning in Ops.factor(left, right): '<' not meaningful for factors## [1] "43" "Gender" NA
## [1] "44" "Glucose_diff" "0"
## [1] "45" "Glucose_max" "0"
## [1] "46" "Glucose_min" "0"
## [1] "47" "HCO3_diff" "0"
## [1] "48" "HCO3_max" "0"
## [1] "49" "HCO3_min" "0"
## [1] "50" "HCT_diff" "0"
## [1] "51" "HCT_max" "0"
## [1] "52" "HCT_min" "0"
## [1] "53" "Height" NA
## [1] "54" "HR_diff" "0"
## [1] "55" "HR_max" "0"
## [1] "56" "HR_min" "0"## Warning in Ops.factor(left, right): '<' not meaningful for factors## [1] "57" "ICUType" NA
## [1] "58" "K_diff" "0"
## [1] "59" "K_max" "0"
## [1] "60" "K_min" "0"
## [1] "61" "Lactate_diff" "0"
## [1] "62" "Lactate_max" "0"
## [1] "63" "Lactate_min" "0"
## [1] "64" "MAP_diff" "0"
## [1] "65" "MAP_max" "0"
## [1] "66" "MAP_min" "0"
## [1] "67" "Mg_diff" "0"
## [1] "68" "Mg_max" "0"
## [1] "69" "Mg_min" "0"
## [1] "70" "Na_diff" "0"
## [1] "71" "Na_max" "0"
## [1] "72" "Na_min" "0"
## [1] "73" "NIDiasABP_diff" NA
## [1] "74" "NIDiasABP_max" NA
## [1] "75" "NIDiasABP_min" NA
## [1] "76" "NIMAP_diff" NA
## [1] "77" "NIMAP_max" NA
## [1] "78" "NIMAP_min" NA
## [1] "79" "NISysABP_diff" NA
## [1] "80" "NISysABP_max" NA
## [1] "81" "NISysABP_min" NA
## [1] "82" "PaCO2_diff" "0"
## [1] "83" "PaCO2_max" "0"
## [1] "84" "PaCO2_min" "0"
## [1] "85" "PaO2_diff" "0"
## [1] "86" "PaO2_max" "0"
## [1] "87" "PaO2_min" "0"
## [1] "88" "pH_diff" "0"
## [1] "89" "pH_max" "0"
## [1] "90" "pH_min" "0"
## [1] "91" "Platelets_diff" "0"
## [1] "92" "Platelets_max" "0"
## [1] "93" "Platelets_min" "0"
## [1] "94" "RespRate_diff" "0"
## [1] "95" "RespRate_max" "0"
## [1] "96" "RespRate_min" "0"
## [1] "97" "SaO2_diff" "0"
## [1] "98" "SaO2_max" "0"
## [1] "99" "SaO2_min" "0"
## [1] "100" "SysABP_diff" NA
## [1] "101" "SysABP_max" NA
## [1] "102" "SysABP_min" NA
## [1] "103" "Temp_diff" "0"
## [1] "104" "Temp_max" "0"
## [1] "105" "Temp_min" "0"
## [1] "106" "TroponinI_diff" "0"
## [1] "107" "TroponinI_max" "0"
## [1] "108" "TroponinI_min" "0"
## [1] "109" "TroponinT_diff" "0"
## [1] "110" "TroponinT_max" "0"
## [1] "111" "TroponinT_min" "0"
## [1] "112" "Urine_diff" "0"
## [1] "113" "Urine_max" "0"
## [1] "114" "Urine_min" "0"
## [1] "115" "WBC_diff" "0"
## [1] "116" "WBC_max" "0"
## [1] "117" "WBC_min" "0"
## [1] "118" "Weight_diff" NA
## [1] "119" "Weight_max" NA
## [1] "120" "Weight_min" NA
## [1] "121" "PFratio" "0" ## Result: negative values in Length_of_stay and SOFA (not listed in initial choice of variables anyway)
# Create a new dataset with the only non-missing data from list of initial variables chosen
# (excluding those with very high missingness i.e. Height, NISysABP_min, NISysABP_max)
nm_icu_model_df1 <- na.omit(subset(icu_patients_df1,
select=c(Days, Status, # the survival object variables
RecordID, # keep record id for reference if needed
in_hospital_death, # from task 1
Age, Gender, ICUType, Weight_max,
Albumin_min, Bilirubin_max,
BUN_max, Creatinine_max,
GCS_max, Glucose_min, Glucose_max,
HCO3_min, HR_min, HR_max, K_min,
K_max, Lactate_max, MAP_min, Na_min,
Na_max, Platelets_min, PFratio, pH_min,
pH_max, RespRate_min, RespRate_max,
Temp_min, Temp_max, TroponinT_max,
TroponinI_max, Urine_min, WBC_min, WBC_max)))
dim(nm_icu_model_df1)## [1] 1915 37Due to the high degree of missingness, NISysABP_min, NISysABP_max and Height variables will be excluded from the multivariate modelling. After removing missing values, the resulting dataset used to fit multivariable models has 1915 observations.
## Fitting multivariable models ##
# Create a function to calculate AIC
calc_aic <- function(model){
AIC <- 2*length(model$coefficients)-2*model$loglik[2]
}
# Full model using all listed initial variables (excluding those with high missingness)
ICU.mv_full <- coxph(Surv(Days, Status) ~
Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max +
BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max +
HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min +
Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max +
RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max +
TroponinI_max + Urine_min + WBC_min + WBC_max,
data = nm_icu_model_df1)
summary(ICU.mv_full)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + Gender + ICUType +
## Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max +
## GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min +
## HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min +
## Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min +
## RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max +
## Urine_min + WBC_min + WBC_max, data = nm_icu_model_df1)
##
## n= 1915, number of events= 721
##
## coef exp(coef) se(coef) z
## Age 0.03317420 1.03373060 0.00293981 11.284
## GenderMale -0.02592987 0.97440342 0.08213299 -0.316
## ICUTypeCardiac Surgery Recovery Unit -0.77268237 0.46177276 0.16528997 -4.675
## ICUTypeMedical ICU 0.31563031 1.37112327 0.11800531 2.675
## ICUTypeSurgical ICU -0.02301483 0.97724799 0.13801760 -0.167
## Weight_max -0.00243670 0.99756627 0.00193453 -1.260
## Albumin_min -0.11881877 0.88796872 0.06628328 -1.793
## Bilirubin_max 0.01439740 1.01450154 0.00797465 1.805
## BUN_max 0.01130860 1.01137279 0.00201088 5.624
## Creatinine_max -0.01482676 0.98528261 0.02766417 -0.536
## GCS_max -0.10623594 0.89921246 0.01452209 -7.315
## Glucose_min -0.00023802 0.99976201 0.00094230 -0.253
## Glucose_max 0.00044814 1.00044824 0.00056329 0.796
## HCO3_min 0.01886028 1.01903926 0.00968401 1.948
## HR_min 0.00591389 1.00593141 0.00306191 1.931
## HR_max 0.00202173 1.00202378 0.00200232 1.010
## K_min 0.06929166 1.07174875 0.08175841 0.848
## K_max -0.03279543 0.96773651 0.04629908 -0.708
## Lactate_max 0.04373789 1.04470849 0.02026084 2.159
## MAP_min -0.00084711 0.99915325 0.00243055 -0.349
## Na_min -0.00760018 0.99242863 0.01840942 -0.413
## Na_max -0.03029393 0.97016034 0.01857343 -1.631
## Platelets_min -0.00033177 0.99966828 0.00042555 -0.780
## PFratio -0.00001688 0.99998312 0.00039515 -0.043
## pH_min -0.48286560 0.61701274 0.20067709 -2.406
## pH_max 0.40316049 1.49654705 0.67511086 0.597
## RespRate_min -0.01676745 0.98337235 0.01305267 -1.285
## RespRate_max 0.00762531 1.00765446 0.00620645 1.229
## Temp_min -0.04991242 0.95131273 0.04838417 -1.032
## Temp_max -0.13691486 0.87204447 0.05738362 -2.386
## TroponinT_max 0.01708332 1.01723007 0.01829875 0.934
## TroponinI_max 0.00253724 1.00254046 0.00399639 0.635
## Urine_min -0.00197615 0.99802581 0.00096945 -2.038
## WBC_min 0.02549144 1.02581913 0.01460170 1.746
## WBC_max -0.01991114 0.98028578 0.01203181 -1.655
## Pr(>|z|)
## Age < 0.0000000000000002 ***
## GenderMale 0.75223
## ICUTypeCardiac Surgery Recovery Unit 0.000002943718242 ***
## ICUTypeMedical ICU 0.00748 **
## ICUTypeSurgical ICU 0.86756
## Weight_max 0.20782
## Albumin_min 0.07304 .
## Bilirubin_max 0.07101 .
## BUN_max 0.000000018688704 ***
## Creatinine_max 0.59199
## GCS_max 0.000000000000256 ***
## Glucose_min 0.80058
## Glucose_max 0.42628
## HCO3_min 0.05147 .
## HR_min 0.05343 .
## HR_max 0.31264
## K_min 0.39671
## K_max 0.47873
## Lactate_max 0.03087 *
## MAP_min 0.72744
## Na_min 0.67972
## Na_max 0.10288
## Platelets_min 0.43561
## PFratio 0.96592
## pH_min 0.01612 *
## pH_max 0.55039
## RespRate_min 0.19893
## RespRate_max 0.21922
## Temp_min 0.30227
## Temp_max 0.01703 *
## TroponinT_max 0.35052
## TroponinI_max 0.52550
## Urine_min 0.04151 *
## WBC_min 0.08085 .
## WBC_max 0.09795 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.0337 0.9674 1.0278 1.0397
## GenderMale 0.9744 1.0263 0.8295 1.1446
## ICUTypeCardiac Surgery Recovery Unit 0.4618 2.1656 0.3340 0.6384
## ICUTypeMedical ICU 1.3711 0.7293 1.0880 1.7279
## ICUTypeSurgical ICU 0.9772 1.0233 0.7456 1.2808
## Weight_max 0.9976 1.0024 0.9938 1.0014
## Albumin_min 0.8880 1.1262 0.7798 1.0112
## Bilirubin_max 1.0145 0.9857 0.9988 1.0305
## BUN_max 1.0114 0.9888 1.0074 1.0154
## Creatinine_max 0.9853 1.0149 0.9333 1.0402
## GCS_max 0.8992 1.1121 0.8740 0.9252
## Glucose_min 0.9998 1.0002 0.9979 1.0016
## Glucose_max 1.0004 0.9996 0.9993 1.0016
## HCO3_min 1.0190 0.9813 0.9999 1.0386
## HR_min 1.0059 0.9941 0.9999 1.0120
## HR_max 1.0020 0.9980 0.9981 1.0060
## K_min 1.0717 0.9331 0.9131 1.2580
## K_max 0.9677 1.0333 0.8838 1.0597
## Lactate_max 1.0447 0.9572 1.0040 1.0870
## MAP_min 0.9992 1.0008 0.9944 1.0039
## Na_min 0.9924 1.0076 0.9573 1.0289
## Na_max 0.9702 1.0308 0.9355 1.0061
## Platelets_min 0.9997 1.0003 0.9988 1.0005
## PFratio 1.0000 1.0000 0.9992 1.0008
## pH_min 0.6170 1.6207 0.4164 0.9143
## pH_max 1.4965 0.6682 0.3985 5.6201
## RespRate_min 0.9834 1.0169 0.9585 1.0089
## RespRate_max 1.0077 0.9924 0.9955 1.0200
## Temp_min 0.9513 1.0512 0.8652 1.0459
## Temp_max 0.8720 1.1467 0.7793 0.9759
## TroponinT_max 1.0172 0.9831 0.9814 1.0544
## TroponinI_max 1.0025 0.9975 0.9947 1.0104
## Urine_min 0.9980 1.0020 0.9961 0.9999
## WBC_min 1.0258 0.9748 0.9969 1.0556
## WBC_max 0.9803 1.0201 0.9574 1.0037
##
## Concordance= 0.743 (se = 0.009 )
## Likelihood ratio test= 518.5 on 35 df, p=<0.0000000000000002
## Wald test = 507.1 on 35 df, p=<0.0000000000000002
## Score (logrank) test = 556 on 35 df, p=<0.0000000000000002# Calculate full model AIC
AIC.mv_full <- calc_aic(ICU.mv_full)
AIC.mv_full #10136## [1] 10135.95# 1st reduced model using all variables with significant log-rank tests
ICU.mv_reduced1 <- coxph(Surv(Days, Status) ~
Age + ICUType + Weight_max + Albumin_min + Bilirubin_max +
BUN_max + Creatinine_max + Glucose_max + HCO3_min +
K_max + Lactate_max + MAP_min + Na_min + pH_min +
pH_max + RespRate_min + RespRate_max + Temp_min +
Temp_max + TroponinT_max + Urine_min,
data = nm_icu_model_df1)
summary(ICU.mv_reduced1)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Weight_max +
## Albumin_min + Bilirubin_max + BUN_max + Creatinine_max +
## Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min +
## Na_min + pH_min + pH_max + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + Urine_min, data = nm_icu_model_df1)
##
## n= 1915, number of events= 721
##
## coef exp(coef) se(coef) z
## Age 0.0312354 1.0317284 0.0028364 11.012
## ICUTypeCardiac Surgery Recovery Unit -0.6478864 0.5231503 0.1526726 -4.244
## ICUTypeMedical ICU 0.3901076 1.4771398 0.1174207 3.322
## ICUTypeSurgical ICU 0.0838899 1.0875091 0.1335289 0.628
## Weight_max -0.0021849 0.9978175 0.0018229 -1.199
## Albumin_min -0.1540079 0.8572653 0.0645077 -2.387
## Bilirubin_max 0.0144855 1.0145910 0.0081080 1.787
## BUN_max 0.0123140 1.0123901 0.0019382 6.353
## Creatinine_max -0.0294390 0.9709901 0.0265352 -1.109
## Glucose_max 0.0001531 1.0001531 0.0004043 0.379
## HCO3_min 0.0174705 1.0176240 0.0092255 1.894
## K_max -0.0253362 0.9749821 0.0363475 -0.697
## Lactate_max 0.0545008 1.0560134 0.0196475 2.774
## MAP_min -0.0012256 0.9987751 0.0023952 -0.512
## Na_min -0.0286393 0.9717669 0.0080801 -3.544
## pH_min -0.6275382 0.5339046 0.1968359 -3.188
## pH_max 0.8969219 2.4520437 0.6400444 1.401
## RespRate_min 0.0163537 1.0164882 0.0116422 1.405
## RespRate_max 0.0124759 1.0125540 0.0056445 2.210
## Temp_min -0.0426614 0.9582358 0.0474244 -0.900
## Temp_max -0.0829817 0.9203680 0.0557570 -1.488
## TroponinT_max 0.0168454 1.0169881 0.0175080 0.962
## Urine_min -0.0025723 0.9974311 0.0009526 -2.700
## Pr(>|z|)
## Age < 0.0000000000000002 ***
## ICUTypeCardiac Surgery Recovery Unit 0.000021992990 ***
## ICUTypeMedical ICU 0.000893 ***
## ICUTypeSurgical ICU 0.529838
## Weight_max 0.230687
## Albumin_min 0.016967 *
## Bilirubin_max 0.074005 .
## BUN_max 0.000000000211 ***
## Creatinine_max 0.267245
## Glucose_max 0.704875
## HCO3_min 0.058262 .
## K_max 0.485769
## Lactate_max 0.005538 **
## MAP_min 0.608865
## Na_min 0.000393 ***
## pH_min 0.001432 **
## pH_max 0.161112
## RespRate_min 0.160113
## RespRate_max 0.027086 *
## Temp_min 0.368351
## Temp_max 0.136678
## TroponinT_max 0.335972
## Urine_min 0.006927 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.0317 0.9692 1.0260 1.0375
## ICUTypeCardiac Surgery Recovery Unit 0.5232 1.9115 0.3879 0.7056
## ICUTypeMedical ICU 1.4771 0.6770 1.1735 1.8594
## ICUTypeSurgical ICU 1.0875 0.9195 0.8371 1.4128
## Weight_max 0.9978 1.0022 0.9943 1.0014
## Albumin_min 0.8573 1.1665 0.7555 0.9728
## Bilirubin_max 1.0146 0.9856 0.9986 1.0308
## BUN_max 1.0124 0.9878 1.0086 1.0162
## Creatinine_max 0.9710 1.0299 0.9218 1.0228
## Glucose_max 1.0002 0.9998 0.9994 1.0009
## HCO3_min 1.0176 0.9827 0.9994 1.0362
## K_max 0.9750 1.0257 0.9079 1.0470
## Lactate_max 1.0560 0.9470 1.0161 1.0975
## MAP_min 0.9988 1.0012 0.9941 1.0035
## Na_min 0.9718 1.0291 0.9565 0.9873
## pH_min 0.5339 1.8730 0.3630 0.7853
## pH_max 2.4520 0.4078 0.6994 8.5968
## RespRate_min 1.0165 0.9838 0.9936 1.0399
## RespRate_max 1.0126 0.9876 1.0014 1.0238
## Temp_min 0.9582 1.0436 0.8732 1.0516
## Temp_max 0.9204 1.0865 0.8251 1.0266
## TroponinT_max 1.0170 0.9833 0.9827 1.0525
## Urine_min 0.9974 1.0026 0.9956 0.9993
##
## Concordance= 0.726 (se = 0.009 )
## Likelihood ratio test= 452.1 on 23 df, p=<0.0000000000000002
## Wald test = 439.8 on 23 df, p=<0.0000000000000002
## Score (logrank) test = 482.2 on 23 df, p=<0.0000000000000002# Calculate 1st reduced model AIC
AIC.mv_reduced1 <- calc_aic(ICU.mv_reduced1)
AIC.mv_reduced1 #10178## [1] 10178.32# 2nd reduced model using all variables significant (using cut off p < 0.1) in ICU.mv_reduced1
# (note using p < 0.1 gained better results than p < 0.05 as a cut off)
ICU.mv_reduced2 <- coxph(Surv(Days, Status) ~
Age + ICUType + Albumin_min + Bilirubin_max + BUN_max +
HCO3_min + Lactate_max + Na_min + pH_min +
RespRate_max + Urine_min,
data = nm_icu_model_df1)
summary(ICU.mv_reduced2)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min +
## pH_min + RespRate_max + Urine_min, data = nm_icu_model_df1)
##
## n= 1915, number of events= 721
##
## coef exp(coef) se(coef) z
## Age 0.0336951 1.0342693 0.0026779 12.583
## ICUTypeCardiac Surgery Recovery Unit -0.7052417 0.4939891 0.1428496 -4.937
## ICUTypeMedical ICU 0.3140214 1.3689190 0.1113657 2.820
## ICUTypeSurgical ICU 0.0067186 1.0067412 0.1273610 0.053
## Albumin_min -0.1529698 0.8581556 0.0634725 -2.410
## Bilirubin_max 0.0146272 1.0147347 0.0079423 1.842
## BUN_max 0.0106532 1.0107102 0.0014018 7.600
## HCO3_min 0.0173644 1.0175161 0.0087596 1.982
## Lactate_max 0.0628071 1.0648214 0.0182291 3.445
## Na_min -0.0252732 0.9750435 0.0073066 -3.459
## pH_min -0.6409326 0.5268009 0.1946101 -3.293
## RespRate_max 0.0143032 1.0144059 0.0047394 3.018
## Urine_min -0.0025693 0.9974340 0.0009383 -2.738
## Pr(>|z|)
## Age < 0.0000000000000002 ***
## ICUTypeCardiac Surgery Recovery Unit 0.0000007935243281 ***
## ICUTypeMedical ICU 0.004806 **
## ICUTypeSurgical ICU 0.957929
## Albumin_min 0.015952 *
## Bilirubin_max 0.065522 .
## BUN_max 0.0000000000000297 ***
## HCO3_min 0.047442 *
## Lactate_max 0.000570 ***
## Na_min 0.000542 ***
## pH_min 0.000990 ***
## RespRate_max 0.002545 **
## Urine_min 0.006177 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.0343 0.9669 1.0289 1.0397
## ICUTypeCardiac Surgery Recovery Unit 0.4940 2.0243 0.3734 0.6536
## ICUTypeMedical ICU 1.3689 0.7305 1.1005 1.7028
## ICUTypeSurgical ICU 1.0067 0.9933 0.7843 1.2922
## Albumin_min 0.8582 1.1653 0.7578 0.9718
## Bilirubin_max 1.0147 0.9855 0.9991 1.0307
## BUN_max 1.0107 0.9894 1.0079 1.0135
## HCO3_min 1.0175 0.9828 1.0002 1.0351
## Lactate_max 1.0648 0.9391 1.0274 1.1036
## Na_min 0.9750 1.0256 0.9612 0.9891
## pH_min 0.5268 1.8983 0.3597 0.7714
## RespRate_max 1.0144 0.9858 1.0050 1.0239
## Urine_min 0.9974 1.0026 0.9956 0.9993
##
## Concordance= 0.724 (se = 0.009 )
## Likelihood ratio test= 439.1 on 13 df, p=<0.0000000000000002
## Wald test = 422.9 on 13 df, p=<0.0000000000000002
## Score (logrank) test = 457.6 on 13 df, p=<0.0000000000000002# Calculate 2nd reduced model AIC
AIC.mv_reduced2 <- calc_aic(ICU.mv_reduced2)
AIC.mv_reduced2 #10171## [1] 10171.34# 3rd reduced model by using step() function on the full model (which had the lowest AIC so far)
ICU.mv_reduced3 <- step(ICU.mv_full, trace=1)## Start: AIC=10135.95
## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min +
## Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max +
## Lactate_max + MAP_min + Na_min + Na_max + Platelets_min +
## PFratio + pH_min + pH_max + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min +
## WBC_min + WBC_max
##
## Df AIC
## - PFratio 1 10134
## - Glucose_min 1 10134
## - Gender 1 10134
## - MAP_min 1 10134
## - Na_min 1 10134
## - Creatinine_max 1 10134
## - pH_max 1 10134
## - TroponinI_max 1 10134
## - K_max 1 10134
## - Platelets_min 1 10135
## - Glucose_max 1 10135
## - K_min 1 10135
## - TroponinT_max 1 10135
## - HR_max 1 10135
## - Temp_min 1 10135
## - RespRate_max 1 10135
## - Weight_max 1 10136
## - RespRate_min 1 10136
## <none> 10136
## - Na_max 1 10137
## - WBC_max 1 10137
## - Bilirubin_max 1 10137
## - WBC_min 1 10137
## - Albumin_min 1 10137
## - HCO3_min 1 10138
## - HR_min 1 10138
## - pH_min 1 10138
## - Lactate_max 1 10138
## - Urine_min 1 10139
## - Temp_max 1 10140
## - BUN_max 1 10163
## - GCS_max 1 10186
## - ICUType 3 10191
## - Age 1 10276
##
## Step: AIC=10133.95
## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min +
## Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max +
## Lactate_max + MAP_min + Na_min + Na_max + Platelets_min +
## pH_min + pH_max + RespRate_min + RespRate_max + Temp_min +
## Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min +
## WBC_max
##
## Df AIC
## - Glucose_min 1 10132
## - Gender 1 10132
## - MAP_min 1 10132
## - Na_min 1 10132
## - Creatinine_max 1 10132
## - pH_max 1 10132
## - TroponinI_max 1 10132
## - K_max 1 10132
## - Platelets_min 1 10133
## - Glucose_max 1 10133
## - K_min 1 10133
## - TroponinT_max 1 10133
## - HR_max 1 10133
## - Temp_min 1 10133
## - RespRate_max 1 10133
## - Weight_max 1 10134
## - RespRate_min 1 10134
## <none> 10134
## - Na_max 1 10135
## - WBC_max 1 10135
## - Bilirubin_max 1 10135
## - WBC_min 1 10135
## - Albumin_min 1 10135
## - HCO3_min 1 10136
## - HR_min 1 10136
## - pH_min 1 10136
## - Lactate_max 1 10136
## - Urine_min 1 10137
## - Temp_max 1 10138
## - BUN_max 1 10162
## - GCS_max 1 10184
## - ICUType 3 10189
## - Age 1 10275
##
## Step: AIC=10132.02
## Surv(Days, Status) ~ Age + Gender + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max +
## MAP_min + Na_min + Na_max + Platelets_min + pH_min + pH_max +
## RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max +
## TroponinI_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - Gender 1 10130
## - MAP_min 1 10130
## - Na_min 1 10130
## - Creatinine_max 1 10130
## - pH_max 1 10130
## - TroponinI_max 1 10130
## - K_max 1 10130
## - Platelets_min 1 10131
## - Glucose_max 1 10131
## - K_min 1 10131
## - TroponinT_max 1 10131
## - HR_max 1 10131
## - Temp_min 1 10131
## - RespRate_max 1 10132
## - Weight_max 1 10132
## - RespRate_min 1 10132
## <none> 10132
## - Na_max 1 10133
## - WBC_max 1 10133
## - Bilirubin_max 1 10133
## - WBC_min 1 10133
## - Albumin_min 1 10133
## - HCO3_min 1 10134
## - HR_min 1 10134
## - pH_min 1 10134
## - Lactate_max 1 10134
## - Urine_min 1 10135
## - Temp_max 1 10136
## - BUN_max 1 10160
## - GCS_max 1 10182
## - ICUType 3 10187
## - Age 1 10273
##
## Step: AIC=10130.11
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max +
## MAP_min + Na_min + Na_max + Platelets_min + pH_min + pH_max +
## RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max +
## TroponinI_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - MAP_min 1 10128
## - Na_min 1 10128
## - Creatinine_max 1 10128
## - pH_max 1 10128
## - K_max 1 10129
## - TroponinI_max 1 10129
## - Platelets_min 1 10129
## - K_min 1 10129
## - Glucose_max 1 10129
## - TroponinT_max 1 10129
## - HR_max 1 10129
## - Temp_min 1 10129
## - RespRate_max 1 10130
## - RespRate_min 1 10130
## <none> 10130
## - Weight_max 1 10130
## - WBC_max 1 10131
## - Na_max 1 10131
## - Bilirubin_max 1 10131
## - WBC_min 1 10131
## - Albumin_min 1 10132
## - HCO3_min 1 10132
## - HR_min 1 10132
## - pH_min 1 10132
## - Lactate_max 1 10133
## - Urine_min 1 10133
## - Temp_max 1 10134
## - BUN_max 1 10158
## - GCS_max 1 10180
## - ICUType 3 10185
## - Age 1 10271
##
## Step: AIC=10128.23
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max +
## Na_min + Na_max + Platelets_min + pH_min + pH_max + RespRate_min +
## RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max +
## Urine_min + WBC_min + WBC_max
##
## Df AIC
## - Na_min 1 10126
## - Creatinine_max 1 10126
## - pH_max 1 10127
## - K_max 1 10127
## - TroponinI_max 1 10127
## - Platelets_min 1 10127
## - K_min 1 10127
## - Glucose_max 1 10127
## - TroponinT_max 1 10127
## - HR_max 1 10127
## - Temp_min 1 10127
## - RespRate_max 1 10128
## - RespRate_min 1 10128
## - Weight_max 1 10128
## <none> 10128
## - WBC_max 1 10129
## - Na_max 1 10129
## - Bilirubin_max 1 10129
## - WBC_min 1 10129
## - Albumin_min 1 10130
## - HCO3_min 1 10130
## - HR_min 1 10130
## - pH_min 1 10130
## - Lactate_max 1 10131
## - Urine_min 1 10131
## - Temp_max 1 10132
## - BUN_max 1 10156
## - GCS_max 1 10179
## - ICUType 3 10184
## - Age 1 10271
##
## Step: AIC=10126.46
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max +
## Na_max + Platelets_min + pH_min + pH_max + RespRate_min +
## RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max +
## Urine_min + WBC_min + WBC_max
##
## Df AIC
## - K_max 1 10125
## - Creatinine_max 1 10125
## - pH_max 1 10125
## - K_min 1 10125
## - Platelets_min 1 10125
## - TroponinI_max 1 10125
## - TroponinT_max 1 10125
## - HR_max 1 10125
## - Glucose_max 1 10125
## - Temp_min 1 10126
## - RespRate_max 1 10126
## - RespRate_min 1 10126
## - Weight_max 1 10126
## <none> 10126
## - WBC_max 1 10127
## - WBC_min 1 10127
## - Bilirubin_max 1 10128
## - Albumin_min 1 10128
## - HCO3_min 1 10128
## - HR_min 1 10128
## - pH_min 1 10129
## - Lactate_max 1 10129
## - Urine_min 1 10130
## - Temp_max 1 10130
## - Na_max 1 10145
## - BUN_max 1 10154
## - GCS_max 1 10177
## - ICUType 3 10183
## - Age 1 10269
##
## Step: AIC=10124.71
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + K_min + Lactate_max + Na_max +
## Platelets_min + pH_min + pH_max + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min +
## WBC_min + WBC_max
##
## Df AIC
## - K_min 1 10123
## - Creatinine_max 1 10123
## - pH_max 1 10123
## - Platelets_min 1 10123
## - TroponinI_max 1 10123
## - Glucose_max 1 10124
## - TroponinT_max 1 10124
## - HR_max 1 10124
## - Temp_min 1 10124
## - RespRate_max 1 10124
## - RespRate_min 1 10124
## - Weight_max 1 10125
## <none> 10125
## - WBC_max 1 10125
## - WBC_min 1 10126
## - Bilirubin_max 1 10126
## - Albumin_min 1 10126
## - HCO3_min 1 10126
## - HR_min 1 10127
## - pH_min 1 10127
## - Lactate_max 1 10127
## - Urine_min 1 10128
## - Temp_max 1 10129
## - Na_max 1 10143
## - BUN_max 1 10152
## - GCS_max 1 10175
## - ICUType 3 10182
## - Age 1 10268
##
## Step: AIC=10123
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_max +
## HCO3_min + HR_min + HR_max + Lactate_max + Na_max + Platelets_min +
## pH_min + pH_max + RespRate_min + RespRate_max + Temp_min +
## Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min +
## WBC_max
##
## Df AIC
## - Creatinine_max 1 10121
## - pH_max 1 10121
## - Platelets_min 1 10121
## - TroponinI_max 1 10122
## - Glucose_max 1 10122
## - TroponinT_max 1 10122
## - HR_max 1 10122
## - Temp_min 1 10122
## - RespRate_max 1 10122
## - Weight_max 1 10123
## - RespRate_min 1 10123
## <none> 10123
## - WBC_max 1 10124
## - Bilirubin_max 1 10124
## - WBC_min 1 10124
## - Albumin_min 1 10124
## - HCO3_min 1 10125
## - HR_min 1 10125
## - pH_min 1 10125
## - Lactate_max 1 10125
## - Urine_min 1 10126
## - Temp_max 1 10127
## - Na_max 1 10143
## - BUN_max 1 10152
## - GCS_max 1 10174
## - ICUType 3 10184
## - Age 1 10268
##
## Step: AIC=10121.29
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min +
## HR_min + HR_max + Lactate_max + Na_max + Platelets_min +
## pH_min + pH_max + RespRate_min + RespRate_max + Temp_min +
## Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min +
## WBC_max
##
## Df AIC
## - pH_max 1 10120
## - Platelets_min 1 10120
## - TroponinI_max 1 10120
## - Glucose_max 1 10120
## - TroponinT_max 1 10120
## - HR_max 1 10120
## - Temp_min 1 10120
## - RespRate_max 1 10120
## - RespRate_min 1 10121
## - Weight_max 1 10121
## <none> 10121
## - Bilirubin_max 1 10122
## - WBC_max 1 10122
## - Albumin_min 1 10123
## - WBC_min 1 10123
## - HCO3_min 1 10123
## - HR_min 1 10123
## - pH_min 1 10124
## - Lactate_max 1 10124
## - Urine_min 1 10124
## - Temp_max 1 10125
## - Na_max 1 10141
## - BUN_max 1 10165
## - GCS_max 1 10173
## - ICUType 3 10182
## - Age 1 10272
##
## Step: AIC=10119.7
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min +
## HR_min + HR_max + Lactate_max + Na_max + Platelets_min +
## pH_min + RespRate_min + RespRate_max + Temp_min + Temp_max +
## TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - TroponinI_max 1 10118
## - Platelets_min 1 10118
## - Glucose_max 1 10118
## - TroponinT_max 1 10119
## - HR_max 1 10119
## - Temp_min 1 10119
## - RespRate_max 1 10119
## <none> 10120
## - RespRate_min 1 10120
## - Weight_max 1 10120
## - Bilirubin_max 1 10121
## - WBC_max 1 10121
## - Albumin_min 1 10121
## - WBC_min 1 10121
## - HR_min 1 10122
## - pH_min 1 10122
## - Lactate_max 1 10122
## - HCO3_min 1 10122
## - Urine_min 1 10122
## - Temp_max 1 10123
## - Na_max 1 10140
## - BUN_max 1 10163
## - GCS_max 1 10174
## - ICUType 3 10182
## - Age 1 10270
##
## Step: AIC=10118.15
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min +
## HR_min + HR_max + Lactate_max + Na_max + Platelets_min +
## pH_min + RespRate_min + RespRate_max + Temp_min + Temp_max +
## TroponinT_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - Platelets_min 1 10117
## - Glucose_max 1 10117
## - TroponinT_max 1 10117
## - Temp_min 1 10117
## - HR_max 1 10118
## <none> 10118
## - RespRate_min 1 10118
## - Weight_max 1 10118
## - RespRate_max 1 10118
## - Bilirubin_max 1 10119
## - WBC_max 1 10119
## - WBC_min 1 10119
## - Albumin_min 1 10120
## - HR_min 1 10120
## - pH_min 1 10120
## - Lactate_max 1 10120
## - Urine_min 1 10121
## - HCO3_min 1 10121
## - Temp_max 1 10122
## - Na_max 1 10138
## - BUN_max 1 10166
## - GCS_max 1 10172
## - ICUType 3 10181
## - Age 1 10268
##
## Step: AIC=10116.63
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + Glucose_max + HCO3_min +
## HR_min + HR_max + Lactate_max + Na_max + pH_min + RespRate_min +
## RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min +
## WBC_min + WBC_max
##
## Df AIC
## - Glucose_max 1 10116
## - TroponinT_max 1 10116
## - Temp_min 1 10116
## - HR_max 1 10116
## <none> 10117
## - Weight_max 1 10117
## - RespRate_min 1 10117
## - RespRate_max 1 10117
## - WBC_min 1 10118
## - WBC_max 1 10118
## - Bilirubin_max 1 10118
## - HR_min 1 10118
## - Albumin_min 1 10118
## - pH_min 1 10119
## - Lactate_max 1 10119
## - Urine_min 1 10119
## - HCO3_min 1 10120
## - Temp_max 1 10120
## - Na_max 1 10136
## - BUN_max 1 10165
## - GCS_max 1 10171
## - ICUType 3 10180
## - Age 1 10268
##
## Step: AIC=10115.63
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max +
## Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max +
## Temp_min + Temp_max + TroponinT_max + Urine_min + WBC_min +
## WBC_max
##
## Df AIC
## - TroponinT_max 1 10115
## - Temp_min 1 10115
## - HR_max 1 10115
## - Weight_max 1 10116
## <none> 10116
## - RespRate_max 1 10116
## - RespRate_min 1 10116
## - WBC_min 1 10116
## - WBC_max 1 10116
## - Bilirubin_max 1 10117
## - Albumin_min 1 10117
## - HR_min 1 10117
## - pH_min 1 10117
## - HCO3_min 1 10118
## - Urine_min 1 10118
## - Temp_max 1 10119
## - Lactate_max 1 10119
## - Na_max 1 10135
## - BUN_max 1 10164
## - GCS_max 1 10171
## - ICUType 3 10182
## - Age 1 10268
##
## Step: AIC=10114.75
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max +
## Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max +
## Temp_min + Temp_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - Temp_min 1 10114
## - HR_max 1 10114
## - Weight_max 1 10115
## <none> 10115
## - RespRate_min 1 10115
## - RespRate_max 1 10115
## - WBC_max 1 10116
## - WBC_min 1 10116
## - Albumin_min 1 10116
## - HR_min 1 10116
## - Bilirubin_max 1 10116
## - HCO3_min 1 10117
## - pH_min 1 10118
## - Urine_min 1 10118
## - Temp_max 1 10118
## - Lactate_max 1 10120
## - Na_max 1 10134
## - BUN_max 1 10163
## - GCS_max 1 10170
## - ICUType 3 10182
## - Age 1 10266
##
## Step: AIC=10113.91
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + HR_max +
## Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max +
## Temp_max + Urine_min + WBC_min + WBC_max
##
## Df AIC
## - HR_max 1 10113
## <none> 10114
## - Weight_max 1 10114
## - RespRate_max 1 10114
## - RespRate_min 1 10114
## - WBC_min 1 10115
## - WBC_max 1 10115
## - HR_min 1 10115
## - Bilirubin_max 1 10115
## - Albumin_min 1 10115
## - HCO3_min 1 10116
## - pH_min 1 10117
## - Urine_min 1 10117
## - Lactate_max 1 10120
## - Temp_max 1 10120
## - Na_max 1 10133
## - BUN_max 1 10162
## - GCS_max 1 10170
## - ICUType 3 10180
## - Age 1 10265
##
## Step: AIC=10113.1
## Surv(Days, Status) ~ Age + ICUType + Weight_max + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max +
## Na_max + pH_min + RespRate_min + RespRate_max + Temp_max +
## Urine_min + WBC_min + WBC_max
##
## Df AIC
## <none> 10113
## - RespRate_min 1 10113
## - RespRate_max 1 10114
## - WBC_max 1 10114
## - Weight_max 1 10114
## - WBC_min 1 10114
## - Bilirubin_max 1 10114
## - Albumin_min 1 10115
## - HCO3_min 1 10115
## - pH_min 1 10116
## - Urine_min 1 10117
## - HR_min 1 10117
## - Temp_max 1 10119
## - Lactate_max 1 10120
## - Na_max 1 10132
## - BUN_max 1 10160
## - GCS_max 1 10169
## - ICUType 3 10182
## - Age 1 10265summary(ICU.mv_reduced3)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Weight_max +
## Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min +
## HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max +
## Temp_max + Urine_min + WBC_min + WBC_max, data = nm_icu_model_df1)
##
## n= 1915, number of events= 721
##
## coef exp(coef) se(coef) z
## Age 0.0337030 1.0342774 0.0028800 11.703
## ICUTypeCardiac Surgery Recovery Unit -0.7585749 0.4683334 0.1455045 -5.213
## ICUTypeMedical ICU 0.2665894 1.3055043 0.1118935 2.383
## ICUTypeSurgical ICU -0.0597760 0.9419755 0.1289216 -0.464
## Weight_max -0.0028717 0.9971324 0.0018165 -1.581
## Albumin_min -0.1217041 0.8854103 0.0647304 -1.880
## Bilirubin_max 0.0151357 1.0152509 0.0078127 1.937
## BUN_max 0.0108042 1.0108628 0.0014283 7.564
## GCS_max -0.1088301 0.8968828 0.0138841 -7.838
## HCO3_min 0.0174338 1.0175867 0.0089639 1.945
## HR_min 0.0064653 1.0064862 0.0026116 2.476
## Lactate_max 0.0570025 1.0586585 0.0186807 3.051
## Na_max -0.0358594 0.9647759 0.0079585 -4.506
## pH_min -0.5088123 0.6012092 0.1823407 -2.790
## RespRate_min -0.0196914 0.9805013 0.0128529 -1.532
## RespRate_max 0.0091086 1.0091502 0.0056285 1.618
## Temp_max -0.1436890 0.8661571 0.0527479 -2.724
## Urine_min -0.0020642 0.9979380 0.0009474 -2.179
## WBC_min 0.0221331 1.0223798 0.0136925 1.616
## WBC_max -0.0178972 0.9822620 0.0114290 -1.566
## Pr(>|z|)
## Age < 0.0000000000000002 ***
## ICUTypeCardiac Surgery Recovery Unit 0.00000018539857563 ***
## ICUTypeMedical ICU 0.01719 *
## ICUTypeSurgical ICU 0.64289
## Weight_max 0.11391
## Albumin_min 0.06008 .
## Bilirubin_max 0.05271 .
## BUN_max 0.00000000000003898 ***
## GCS_max 0.00000000000000456 ***
## HCO3_min 0.05179 .
## HR_min 0.01330 *
## Lactate_max 0.00228 **
## Na_max 0.00000661319368369 ***
## pH_min 0.00526 **
## RespRate_min 0.12551
## RespRate_max 0.10560
## Temp_max 0.00645 **
## Urine_min 0.02934 *
## WBC_min 0.10600
## WBC_max 0.11736
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.0343 0.9669 1.0285 1.0401
## ICUTypeCardiac Surgery Recovery Unit 0.4683 2.1352 0.3521 0.6229
## ICUTypeMedical ICU 1.3055 0.7660 1.0484 1.6256
## ICUTypeSurgical ICU 0.9420 1.0616 0.7316 1.2128
## Weight_max 0.9971 1.0029 0.9936 1.0007
## Albumin_min 0.8854 1.1294 0.7799 1.0052
## Bilirubin_max 1.0153 0.9850 0.9998 1.0309
## BUN_max 1.0109 0.9893 1.0080 1.0137
## GCS_max 0.8969 1.1150 0.8728 0.9216
## HCO3_min 1.0176 0.9827 0.9999 1.0356
## HR_min 1.0065 0.9936 1.0013 1.0117
## Lactate_max 1.0587 0.9446 1.0206 1.0981
## Na_max 0.9648 1.0365 0.9498 0.9799
## pH_min 0.6012 1.6633 0.4205 0.8595
## RespRate_min 0.9805 1.0199 0.9561 1.0055
## RespRate_max 1.0092 0.9909 0.9981 1.0203
## Temp_max 0.8662 1.1545 0.7811 0.9605
## Urine_min 0.9979 1.0021 0.9961 0.9998
## WBC_min 1.0224 0.9781 0.9953 1.0502
## WBC_max 0.9823 1.0181 0.9605 1.0045
##
## Concordance= 0.741 (se = 0.009 )
## Likelihood ratio test= 511.4 on 20 df, p=<0.0000000000000002
## Wald test = 497.9 on 20 df, p=<0.0000000000000002
## Score (logrank) test = 541.4 on 20 df, p=<0.0000000000000002## Interestingly: GCS_max, HR_min & Na_max have worked their way back in (not significant on log-rank)
# Calculate 3rd reduced model AIC
AIC.mv_reduced3 <- calc_aic(ICU.mv_reduced3)
AIC.mv_reduced3 #10113## [1] 10113.1# 4th reduced model using significant variables (using cut off p < 0.1) from ICU.mv_reduced3
ICU.mv_reduced4 <- coxph(Surv(Days, Status) ~
Age + ICUType + Albumin_min + Bilirubin_max + BUN_max +
GCS_max + HCO3_min + HR_min + Lactate_max + Na_max +
pH_min + Temp_max + Urine_min,
data = nm_icu_model_df1)
summary(ICU.mv_reduced4)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType + Albumin_min +
## Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max +
## Na_max + pH_min + Temp_max + Urine_min, data = nm_icu_model_df1)
##
## n= 1915, number of events= 721
##
## coef exp(coef) se(coef) z
## Age 0.0350388 1.0356599 0.0027689 12.654
## ICUTypeCardiac Surgery Recovery Unit -0.7506795 0.4720457 0.1436016 -5.228
## ICUTypeMedical ICU 0.2966536 1.3453492 0.1113497 2.664
## ICUTypeSurgical ICU -0.0489970 0.9521840 0.1281524 -0.382
## Albumin_min -0.0975028 0.9070998 0.0640981 -1.521
## Bilirubin_max 0.0176857 1.0178431 0.0075944 2.329
## BUN_max 0.0103542 1.0104080 0.0013927 7.435
## GCS_max -0.1025152 0.9025644 0.0122724 -8.353
## HCO3_min 0.0169520 1.0170965 0.0086722 1.955
## HR_min 0.0064894 1.0065105 0.0025183 2.577
## Lactate_max 0.0560927 1.0576957 0.0185001 3.032
## Na_max -0.0362758 0.9643743 0.0078693 -4.610
## pH_min -0.4684910 0.6259461 0.1892577 -2.475
## Temp_max -0.1537885 0.8574533 0.0518889 -2.964
## Urine_min -0.0019496 0.9980523 0.0009352 -2.085
## Pr(>|z|)
## Age < 0.0000000000000002 ***
## ICUTypeCardiac Surgery Recovery Unit 0.000000171804359 ***
## ICUTypeMedical ICU 0.00772 **
## ICUTypeSurgical ICU 0.70221
## Albumin_min 0.12822
## Bilirubin_max 0.01987 *
## BUN_max 0.000000000000105 ***
## GCS_max < 0.0000000000000002 ***
## HCO3_min 0.05061 .
## HR_min 0.00997 **
## Lactate_max 0.00243 **
## Na_max 0.000004031402074 ***
## pH_min 0.01331 *
## Temp_max 0.00304 **
## Urine_min 0.03710 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## Age 1.0357 0.9656 1.0301 1.0413
## ICUTypeCardiac Surgery Recovery Unit 0.4720 2.1184 0.3562 0.6255
## ICUTypeMedical ICU 1.3453 0.7433 1.0816 1.6735
## ICUTypeSurgical ICU 0.9522 1.0502 0.7407 1.2241
## Albumin_min 0.9071 1.1024 0.8000 1.0285
## Bilirubin_max 1.0178 0.9825 1.0028 1.0331
## BUN_max 1.0104 0.9897 1.0077 1.0132
## GCS_max 0.9026 1.1080 0.8811 0.9245
## HCO3_min 1.0171 0.9832 1.0000 1.0345
## HR_min 1.0065 0.9935 1.0016 1.0115
## Lactate_max 1.0577 0.9455 1.0200 1.0968
## Na_max 0.9644 1.0369 0.9496 0.9794
## pH_min 0.6259 1.5976 0.4320 0.9071
## Temp_max 0.8575 1.1662 0.7745 0.9492
## Urine_min 0.9981 1.0020 0.9962 0.9999
##
## Concordance= 0.738 (se = 0.009 )
## Likelihood ratio test= 501.6 on 15 df, p=<0.0000000000000002
## Wald test = 481.3 on 15 df, p=<0.0000000000000002
## Score (logrank) test = 519.6 on 15 df, p=<0.0000000000000002# Calculate 4th reduced model AIC
AIC.mv_reduced4 <- calc_aic(ICU.mv_reduced4)
AIC.mv_reduced4 #10112## [1] 10112.83# Comparing models with LRT
lapply(list(ICU.mv_reduced1, ICU.mv_reduced2, ICU.mv_reduced3, ICU.mv_reduced4),
function(reduced) {print(anova(ICU.mv_full, reduced))} )## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min + Na_min + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5066.2 66.37 12 0.00000000152 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min + pH_min + RespRate_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5072.7 79.388 22 0.00000002043 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + Temp_max + Urine_min + WBC_min + WBC_max
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5036.5 7.1483 15 0.9534
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + Temp_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5041.4 16.877 20 0.6609## [[1]]
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + Glucose_max + HCO3_min + K_max + Lactate_max + MAP_min + Na_min + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5066.2 66.37 12 0.00000000152 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[2]]
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + HCO3_min + Lactate_max + Na_min + pH_min + RespRate_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5072.7 79.388 22 0.00000002043 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## [[3]]
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + RespRate_min + RespRate_max + Temp_max + Urine_min + WBC_min + WBC_max
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5036.5 7.1483 15 0.9534
##
## [[4]]
## Analysis of Deviance Table
## Cox model: response is Surv(Days, Status)
## Model 1: ~ Age + Gender + ICUType + Weight_max + Albumin_min + Bilirubin_max + BUN_max + Creatinine_max + GCS_max + Glucose_min + Glucose_max + HCO3_min + HR_min + HR_max + K_min + K_max + Lactate_max + MAP_min + Na_min + Na_max + Platelets_min + PFratio + pH_min + pH_max + RespRate_min + RespRate_max + Temp_min + Temp_max + TroponinT_max + TroponinI_max + Urine_min + WBC_min + WBC_max
## Model 2: ~ Age + ICUType + Albumin_min + Bilirubin_max + BUN_max + GCS_max + HCO3_min + HR_min + Lactate_max + Na_max + pH_min + Temp_max + Urine_min
## loglik Chisq Df P(>|Chi|)
## 1 -5033.0
## 2 -5041.4 16.877 20 0.6609## Results: reduced1 and reduced2 - reject the null hypothesis that the reduced models are better (they are worse)
## reduced3 and reduced4 - DONT reject the null hypothesis
## --> therefore the reduced models are better than the full model (matches our AICs)
# Print the AICs all together to review
aic_output <- c(AIC.mv_full, AIC.mv_reduced1, AIC.mv_reduced2, AIC.mv_reduced3, AIC.mv_reduced4)
names(aic_output) <- c('Full AIC', 'Reduced 1 AIC', 'Reduced 2 AIC', 'Reduced 3 AIC', 'Reduced 4 AIC')
print(aic_output)## Full AIC Reduced 1 AIC Reduced 2 AIC Reduced 3 AIC Reduced 4 AIC
## 10135.95 10178.32 10171.34 10113.10 10112.83## Decision: use ICU.mv_reduced4 as the provisional final model (lowest AIC and non-significant LRT)
## Note: the model 3 still has the better likelihood statistic than Model 4, but we choose model 4 for parsimonySelecting a multivariable Cox proportional hazards model:
Full model - a model with all selected variables (excluding those with high degree of missingness) has been fitted. In the resulting fitted model, Age, ICU type, BUN_max, GCS_max, are highly significant. Lactate_max, pH_min, Temp_max and urine_min are also significant at 5% significance level. Furthermore, Albumin_min, Bilirubin_max, HCO3_min, HR_min, WBC_min and WBC_max are significant at 10% significance level. The resulting model has a maximised likelihood of 518.5. The log rank test statistic is highly significant (p-value close to 0), indicating that the variables in the full model have significant explanatory power on ICU population survival. Note, the AIC of the full model is 10,136.
Reduced Model 1 - for parsimony, we look for a reduced model with fewer variables than can adequately explain survival rates for the ICU population. Our first attempt is to only include variables that resulted in a significant log rank test for the respective univariate models. Since the reduced model is nested in the full model, we use a likelihood ratio test to compare the two model. We reject the null hypothesis (p-value is 0.000000000152) and conclude that the full model is a better fit to the data. This conclusion is echoed when comparing the models’ AICs - the reduced model has a higher AIC of 10,178.
Reduced Model 2 - the second attempt, reduces the Reduced Model 1 by only including variables that were significant at a 10% significance level. We can again use a likelihood ratio test to compare this model with the full model as the models are nested. We reject the null hypothesis (p-value is 0.00000002043) and conclude that the full model is a better fit to the data. Whilst the AIC for Model 2 (10,171) is lower than for Model 1, it is higher than the Full Model, which leads to the same conclusion as the LRT test.
Reduced Model 3 - the third attempt starts with the full model and uses the step function to search the model space for a model with a better fit and fewer covariates. After 17 iterations, the reduced model includes 18 covariates. Interestingly, GCS_max, HR_min & Na_max are now being included in the model despite the non-significant log rank tests for the univariate models. When compared with the full model, the null hypothesis of the LRT test (p-value = 0.95)is accepted and we can conclude that the reduced model is a better fit to the data than the full model. Furthermore, the AIC is reduced to 10,113.
Reduced Model 4 - in this model, we take Model 3 and only include the significant variables at 10% significance level (i.e. removed Weight_max, RespRate_min, respRate_max, WBC_min, WBC_max). When compared with the full model, the null hypothesis of the LRT test (p-value = 0.66) is accepted and we can conclude that the reduced model is a better fit to the data than the full model. Furthermore, the AIC is reduced to 10,112 which is slightly lower than the AIC for Reduced Model 3.
Cox proportional hazards model assumption checking:
## Testing assumptions ##
# Testing for proportional hazards assumption of ICU.mv_reduced4 using cox.zph()
cox.zph(ICU.mv_reduced4, terms=FALSE)## chisq df p
## Age 1.04471 1 0.30673
## ICUTypeCardiac Surgery Recovery Unit 10.34626 1 0.00130
## ICUTypeMedical ICU 0.00654 1 0.93553
## ICUTypeSurgical ICU 4.60886 1 0.03181
## Albumin_min 12.67940 1 0.00037
## Bilirubin_max 11.96366 1 0.00054
## BUN_max 0.93552 1 0.33343
## GCS_max 25.48016 1 0.000000446955
## HCO3_min 25.17651 1 0.000000523154
## HR_min 4.47650 1 0.03436
## Lactate_max 32.07772 1 0.000000014813
## Na_max 0.05096 1 0.82140
## pH_min 0.41234 1 0.52078
## Temp_max 1.89556 1 0.16858
## Urine_min 3.24395 1 0.07169
## GLOBAL 89.96094 15 0.000000000001## Result: statistically significant global test, therefore the proportional hazards model is violated
## (the variables that violate are: ICUType, Albumin_min, Bilirubin_max, GCS_max, HCO3_min, HR_min, Lactate_max)
# Including time x covariate interactions to fix proportional hazards for problematic variables
# Split the dataset at 90 days (~ 3 months)
# Suspect there may be some systematic differences in patients who survive less than or greater than 3 months after ICU admission
ICU.split <- survSplit(Surv(Days, Status) ~ ., data = nm_icu_model_df1, cut=c(90), episode= "tgroup", id="id2")
head(ICU.split)## RecordID in_hospital_death Age Gender ICUType
## 1 132540 0 76 Male Cardiac Surgery Recovery Unit
## 2 132540 0 76 Male Cardiac Surgery Recovery Unit
## 3 132541 0 44 Female Medical ICU
## 4 132541 0 44 Female Medical ICU
## 5 132543 0 68 Male Medical ICU
## 6 132543 0 68 Male Medical ICU
## Weight_max Albumin_min Bilirubin_max BUN_max Creatinine_max GCS_max
## 1 80.6 2.2 1.2 18 1.2 15
## 2 80.6 2.2 1.2 18 1.2 15
## 3 56.7 2.3 3.0 8 0.4 8
## 4 56.7 2.3 3.0 8 0.4 8
## 5 84.6 4.4 0.2 23 0.9 15
## 6 84.6 4.4 0.2 23 0.9 15
## Glucose_min Glucose_max HCO3_min HR_min HR_max K_min K_max Lactate_max
## 1 105 105 21 80 88 4.3 4.3 2.9
## 2 105 105 21 80 88 4.3 4.3 2.9
## 3 119 141 24 57 113 3.3 8.6 1.9
## 4 119 141 24 57 113 3.3 8.6 1.9
## 5 106 129 27 57 88 4.0 4.2 1.2
## 6 106 129 27 57 88 4.0 4.2 1.2
## MAP_min Na_min Na_max Platelets_min PFratio pH_min pH_max RespRate_min
## 1 43 139 139 164 89 7.34 7.45 11
## 2 43 139 139 164 89 7.34 7.45 11
## 3 71 137 140 72 65 7.51 7.51 18
## 4 71 137 140 72 65 7.51 7.51 18
## 5 72 140 141 315 64 7.47 7.51 12
## 6 72 140 141 315 64 7.47 7.51 12
## RespRate_max Temp_min Temp_max TroponinT_max TroponinI_max Urine_min WBC_min
## 1 36 34.5 37.9 0.43 31.7 0 7.4
## 2 36 34.5 37.9 0.43 31.7 0 7.4
## 3 33 36.7 39.0 1.55 33.4 30 3.7
## 4 33 36.7 39.0 1.55 33.4 30 3.7
## 5 21 35.1 36.7 0.10 5.9 100 8.8
## 6 21 35.1 36.7 0.10 5.9 100 8.8
## WBC_max id2 tstart Days Status tgroup
## 1 13.1 1 0 90 0 1
## 2 13.1 1 90 2408 0 2
## 3 4.2 2 0 90 0 1
## 4 4.2 2 90 2408 0 2
## 5 11.5 3 0 90 0 1
## 6 11.5 3 90 575 1 2# Fit the model with time x covariate interactions
ICU.mv_reduced4.split <- coxph(Surv(Days, Status) ~
Age + ICUType:strata(tgroup) +
Albumin_min:strata(tgroup) +
Bilirubin_max:strata(tgroup) + BUN_max +
GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
HR_min:strata(tgroup) +
Lactate_max:strata(tgroup) + Na_max + pH_min +
Temp_max + Urine_min,
data = ICU.split)
summary(ICU.mv_reduced4.split)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) +
## Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) +
## BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
## HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max +
## pH_min + Temp_max + Urine_min, data = ICU.split)
##
## n= 3448, number of events= 721
##
## coef
## Age 0.0346090
## BUN_max 0.0102853
## Na_max -0.0373177
## pH_min -0.4234153
## Temp_max -0.1532807
## Urine_min -0.0018609
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.0334824
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1587488
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.1907664
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.0755461
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3034695
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5346959
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min -0.2316071
## strata(tgroup)tgroup=2:Albumin_min 0.0295442
## strata(tgroup)tgroup=1:Bilirubin_max 0.0294162
## strata(tgroup)tgroup=2:Bilirubin_max -0.0166200
## strata(tgroup)tgroup=1:GCS_max -0.1284553
## strata(tgroup)tgroup=2:GCS_max -0.0686016
## strata(tgroup)tgroup=1:HCO3_min -0.0017832
## strata(tgroup)tgroup=2:HCO3_min 0.0399073
## strata(tgroup)tgroup=1:HR_min 0.0092707
## strata(tgroup)tgroup=2:HR_min 0.0021339
## strata(tgroup)tgroup=1:Lactate_max 0.0847352
## strata(tgroup)tgroup=2:Lactate_max -0.0122143
## exp(coef)
## Age 1.0352149
## BUN_max 1.0103384
## Na_max 0.9633700
## pH_min 0.6548066
## Temp_max 0.8578889
## Urine_min 0.9981409
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0340493
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3138787
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2101767
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0784730
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7382524
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7069291
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7932578
## strata(tgroup)tgroup=2:Albumin_min 1.0299849
## strata(tgroup)tgroup=1:Bilirubin_max 1.0298531
## strata(tgroup)tgroup=2:Bilirubin_max 0.9835173
## strata(tgroup)tgroup=1:GCS_max 0.8794529
## strata(tgroup)tgroup=2:GCS_max 0.9336986
## strata(tgroup)tgroup=1:HCO3_min 0.9982184
## strata(tgroup)tgroup=2:HCO3_min 1.0407143
## strata(tgroup)tgroup=1:HR_min 1.0093138
## strata(tgroup)tgroup=2:HR_min 1.0021362
## strata(tgroup)tgroup=1:Lactate_max 1.0884289
## strata(tgroup)tgroup=2:Lactate_max 0.9878600
## se(coef) z
## Age 0.0027578 12.550
## BUN_max 0.0013839 7.432
## Na_max 0.0078838 -4.733
## pH_min 0.1948427 -2.173
## Temp_max 0.0519571 -2.950
## Urine_min 0.0009391 -1.982
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.1693702 0.198
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2046760 -5.661
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.1313555 1.452
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 0.0000000 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.1898386 0.398
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.1780409 -1.704
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.1497039 3.572
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 0.0000000 NA
## strata(tgroup)tgroup=1:Albumin_min 0.0876911 -2.641
## strata(tgroup)tgroup=2:Albumin_min 0.0932320 0.317
## strata(tgroup)tgroup=1:Bilirubin_max 0.0081990 3.588
## strata(tgroup)tgroup=2:Bilirubin_max 0.0176978 -0.939
## strata(tgroup)tgroup=1:GCS_max 0.0157474 -8.157
## strata(tgroup)tgroup=2:GCS_max 0.0190971 -3.592
## strata(tgroup)tgroup=1:HCO3_min 0.0116061 -0.154
## strata(tgroup)tgroup=2:HCO3_min 0.0122847 3.249
## strata(tgroup)tgroup=1:HR_min 0.0032363 2.865
## strata(tgroup)tgroup=2:HR_min 0.0038392 0.556
## strata(tgroup)tgroup=1:Lactate_max 0.0205997 4.113
## strata(tgroup)tgroup=2:Lactate_max 0.0345008 -0.354
## Pr(>|z|)
## Age < 0.0000000000000002
## BUN_max 0.000000000000107052
## Na_max 0.000002207204558216
## pH_min 0.029772
## Temp_max 0.003176
## Urine_min 0.047532
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.843289
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015015891605
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.146421
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.690668
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.088289
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.000355
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.008262
## strata(tgroup)tgroup=2:Albumin_min 0.751328
## strata(tgroup)tgroup=1:Bilirubin_max 0.000334
## strata(tgroup)tgroup=2:Bilirubin_max 0.347680
## strata(tgroup)tgroup=1:GCS_max 0.000000000000000343
## strata(tgroup)tgroup=2:GCS_max 0.000328
## strata(tgroup)tgroup=1:HCO3_min 0.877893
## strata(tgroup)tgroup=2:HCO3_min 0.001160
## strata(tgroup)tgroup=1:HR_min 0.004176
## strata(tgroup)tgroup=2:HR_min 0.578339
## strata(tgroup)tgroup=1:Lactate_max 0.000038982884543304
## strata(tgroup)tgroup=2:Lactate_max 0.723318
##
## Age ***
## BUN_max ***
## Na_max ***
## pH_min *
## Temp_max **
## Urine_min *
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
## ICUTypeMedical ICU:strata(tgroup)tgroup=1
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 ***
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2
## strata(tgroup)tgroup=1:Albumin_min **
## strata(tgroup)tgroup=2:Albumin_min
## strata(tgroup)tgroup=1:Bilirubin_max ***
## strata(tgroup)tgroup=2:Bilirubin_max
## strata(tgroup)tgroup=1:GCS_max ***
## strata(tgroup)tgroup=2:GCS_max ***
## strata(tgroup)tgroup=1:HCO3_min
## strata(tgroup)tgroup=2:HCO3_min **
## strata(tgroup)tgroup=1:HR_min **
## strata(tgroup)tgroup=2:HR_min
## strata(tgroup)tgroup=1:Lactate_max ***
## strata(tgroup)tgroup=2:Lactate_max
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef)
## Age 1.0352
## BUN_max 1.0103
## Na_max 0.9634
## pH_min 0.6548
## Temp_max 0.8579
## Urine_min 0.9981
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0340
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2102
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0785
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7383
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7069
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7933
## strata(tgroup)tgroup=2:Albumin_min 1.0300
## strata(tgroup)tgroup=1:Bilirubin_max 1.0299
## strata(tgroup)tgroup=2:Bilirubin_max 0.9835
## strata(tgroup)tgroup=1:GCS_max 0.8795
## strata(tgroup)tgroup=2:GCS_max 0.9337
## strata(tgroup)tgroup=1:HCO3_min 0.9982
## strata(tgroup)tgroup=2:HCO3_min 1.0407
## strata(tgroup)tgroup=1:HR_min 1.0093
## strata(tgroup)tgroup=2:HR_min 1.0021
## strata(tgroup)tgroup=1:Lactate_max 1.0884
## strata(tgroup)tgroup=2:Lactate_max 0.9879
## exp(-coef)
## Age 0.9660
## BUN_max 0.9898
## Na_max 1.0380
## pH_min 1.5272
## Temp_max 1.1657
## Urine_min 1.0019
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.9671
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 3.1859
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.8263
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.9272
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.3546
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5858
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 1.2606
## strata(tgroup)tgroup=2:Albumin_min 0.9709
## strata(tgroup)tgroup=1:Bilirubin_max 0.9710
## strata(tgroup)tgroup=2:Bilirubin_max 1.0168
## strata(tgroup)tgroup=1:GCS_max 1.1371
## strata(tgroup)tgroup=2:GCS_max 1.0710
## strata(tgroup)tgroup=1:HCO3_min 1.0018
## strata(tgroup)tgroup=2:HCO3_min 0.9609
## strata(tgroup)tgroup=1:HR_min 0.9908
## strata(tgroup)tgroup=2:HR_min 0.9979
## strata(tgroup)tgroup=1:Lactate_max 0.9188
## strata(tgroup)tgroup=2:Lactate_max 1.0123
## lower .95 upper .95
## Age 1.0296 1.0408
## BUN_max 1.0076 1.0131
## Na_max 0.9486 0.9784
## pH_min 0.4470 0.9593
## Temp_max 0.7748 0.9499
## Urine_min 0.9963 1.0000
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.7419 1.4412
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2102 0.4688
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.9355 1.5655
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7434 1.5646
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.5208 1.0465
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.2729 2.2890
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA NA
## strata(tgroup)tgroup=1:Albumin_min 0.6680 0.9420
## strata(tgroup)tgroup=2:Albumin_min 0.8580 1.2365
## strata(tgroup)tgroup=1:Bilirubin_max 1.0134 1.0465
## strata(tgroup)tgroup=2:Bilirubin_max 0.9500 1.0182
## strata(tgroup)tgroup=1:GCS_max 0.8527 0.9070
## strata(tgroup)tgroup=2:GCS_max 0.8994 0.9693
## strata(tgroup)tgroup=1:HCO3_min 0.9758 1.0212
## strata(tgroup)tgroup=2:HCO3_min 1.0160 1.0661
## strata(tgroup)tgroup=1:HR_min 1.0029 1.0157
## strata(tgroup)tgroup=2:HR_min 0.9946 1.0097
## strata(tgroup)tgroup=1:Lactate_max 1.0454 1.1333
## strata(tgroup)tgroup=2:Lactate_max 0.9233 1.0570
##
## Concordance= 0.748 (se = 0.009 )
## Likelihood ratio test= 564.7 on 24 df, p=<0.0000000000000002
## Wald test = 544.8 on 24 df, p=<0.0000000000000002
## Score (logrank) test = 593.4 on 24 df, p=<0.0000000000000002# evaluating the proportional hazards assumption again, for the model with time x covariate interactions
cox.zph(ICU.mv_reduced4.split, terms=FALSE)## chisq df p
## Age 0.16638 1 0.6833
## BUN_max 0.02835 1 0.8663
## Na_max 0.52712 1 0.4678
## pH_min 0.20377 1 0.6517
## Temp_max 0.36572 1 0.5453
## Urine_min 1.64748 1 0.1993
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.00282 1 0.9576
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.68770 1 0.4069
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.00532 1 0.9419
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.11821 1 0.7310
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 2.10958 1 0.1464
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.58893 1 0.4428
## strata(tgroup)tgroup=1:Albumin_min 2.32455 1 0.1273
## strata(tgroup)tgroup=2:Albumin_min 0.00195 1 0.9648
## strata(tgroup)tgroup=1:Bilirubin_max 0.92725 1 0.3356
## strata(tgroup)tgroup=2:Bilirubin_max 3.38839 1 0.0657
## strata(tgroup)tgroup=1:GCS_max 10.61588 1 0.0011
## strata(tgroup)tgroup=2:GCS_max 2.53281 1 0.1115
## strata(tgroup)tgroup=1:HCO3_min 4.83676 1 0.0279
## strata(tgroup)tgroup=2:HCO3_min 1.56563 1 0.2108
## strata(tgroup)tgroup=1:HR_min 0.97301 1 0.3239
## strata(tgroup)tgroup=2:HR_min 0.32407 1 0.5692
## strata(tgroup)tgroup=1:Lactate_max 5.00208 1 0.0253
## strata(tgroup)tgroup=2:Lactate_max 5.91846 1 0.0150
## GLOBAL 35.16653 24 0.0660## Result: the global test is now insignificant (p = 0.07)
# Checking Linearity by observing Martingale residuals
# Refit the chosen model with any factor variables re-coded as numeric
# to allow the ggcoxfunctional() function to work
ICU.mv_reduced4.nofactor <- coxph(Surv(Days, Status) ~
Age + as.numeric(ICUType) + Albumin_min + Bilirubin_max + BUN_max +
GCS_max + HCO3_min + HR_min + Lactate_max + Na_max +
pH_min + Temp_max + Urine_min,
data = nm_icu_model_df1)
ggcoxfunctional(ICU.mv_reduced4.nofactor, nm_icu_model_df1)
## Result: they don't look particularly linear... especially with laboratory values very far from the reference ranges
## (likely few observations in this range / potential outliers)
# Check linearity of the model as a whole
ggcoxdiagnostics(ICU.mv_reduced4, type = "martingale", linear.predictions = FALSE, ggtheme = theme_bw()) ## `geom_smooth()` using formula 'y ~ x'
## Result: appears reasonably linear with with 2 large negative outliers
## (large negative interpretation = 'lived too long')
# Examine the observations with very large negative residuals (< -3)
resid(ICU.mv_reduced4)[resid(ICU.mv_reduced4) < -3]## 1511 1929
## -4.197771 -3.207614icu_patients_df1[c(1511,1929),]## RecordID Length_of_stay SAPS1 SOFA Survival in_hospital_death Days Status
## 1511 136398 51 22 10 NA 0 2408 FALSE
## 1929 137433 23 NA 7 NA 0 2408 FALSE
## Age Albumin_diff Albumin_max Albumin_min ALP_diff ALP_max ALP_min ALT_diff
## 1511 70 0.0186633 3.0 3.0 50.85204 45 74 105.4462
## 1929 78 0.6813367 2.3 2.3 57.14796 153 153 138.5538
## ALT_max ALT_min AST_diff AST_max AST_min Bilirubin_diff Bilirubin_max
## 1511 40 15 151.3527 18 57 1.364039 0.9
## 1929 259 259 203.6473 373 373 4.935961 6.7
## Bilirubin_min BUN_diff BUN_max BUN_min Cholesterol_diff Cholesterol_max
## 1511 0.4 99.47295 124 120 9.422764 147
## 1929 6.7 97.47295 122 122 81.422764 75
## Cholesterol_min Creatinine_diff Creatinine_max Creatinine_min DiasABP_diff
## 1511 147 5.167554 6.4 5.8 11.54421
## 1929 101 2.967554 4.2 4.2 NA
## DiasABP_max DiasABP_min FiO2_diff FiO2_max FiO2_min GCS_diff GCS_max
## 1511 67 47 0.4480799 1 0.4 6.244029 9
## 1929 NA NA 0.4480799 1 1.0 3.755971 15
## GCS_min Gender Glucose_diff Glucose_max Glucose_min HCO3_diff HCO3_max
## 1511 5 Female 142.14446 282 41 15.772548 10
## 1929 15 Male 66.85554 73 73 0.772548 22
## HCO3_min HCT_diff HCT_max HCT_min Height HR_diff HR_max HR_min
## 1511 7 10.460129 31.5 20.5 165.1 45.07789 70 42
## 1929 22 4.760129 26.2 26.2 177.8 27.07789 65 60
## ICUType K_diff K_max K_min Lactate_diff Lactate_max Lactate_min
## 1511 Medical ICU 0.6352066 3.9 3.5 4.803596 7.6 7.6
## 1929 Medical ICU 0.1352066 4.0 4.0 2.203596 5.0 1.6
## MAP_diff MAP_max MAP_min Mg_diff Mg_max Mg_min Na_diff Na_max Na_min
## 1511 120.23164 198 55 0.1842982 2.0 1.8 8.206607 133 131
## 1929 19.76836 58 65 0.6157018 2.6 2.6 6.206607 133 133
## NIDiasABP_diff NIDiasABP_max NIDiasABP_min NIMAP_diff NIMAP_max NIMAP_min
## 1511 20.49101 72 37 21.38069 84.67 54.33
## 1929 31.49101 82 26 24.04069 93.00 51.67
## NISysABP_diff NISysABP_max NISysABP_min PaCO2_diff PaCO2_max PaCO2_min
## 1511 37.69875 126 79 25.335797 22 15
## 1929 18.69875 119 98 4.335797 40 36
## PaO2_diff PaO2_max PaO2_min pH_diff pH_max pH_min Platelets_diff
## 1511 282.3821 441 120 0.14988624 7.31 7.22 77.76931
## 1929 108.6179 107 50 0.07988624 7.31 7.29 154.23069
## Platelets_max Platelets_min RespRate_diff RespRate_max RespRate_min
## 1511 150 112 10.65142 30 10
## 1929 344 344 11.65142 31 17
## SaO2_diff SaO2_max SaO2_min SysABP_diff SysABP_max SysABP_min Temp_diff
## 1511 0.7539211 98 98 42.3105 126 74 2.574083
## 1929 2.2460789 99 95 NA NA NA 1.174083
## Temp_max Temp_min TroponinI_diff TroponinI_max TroponinI_min
## 1511 36.1 34.4 1.542945 3.9 3.9
## 1929 37.9 35.8 3.742945 3.9 1.7
## TroponinT_diff TroponinT_max TroponinT_min Urine_diff Urine_max Urine_min
## 1511 0.6185006 0.27 0.05 99.21758 70 0
## 1929 3.3414994 4.01 1.67 99.21758 120 0
## WBC_diff WBC_max WBC_min Weight_diff Weight_max Weight_min PFratio
## 1511 3.7331524 9.8 8.4 2.499878 78.2 78.2 120
## 1929 0.6668476 12.8 12.8 4.699878 76.0 76.0 50## Interpretation: looks like they were relatively elderly with long lengths of stay
## - one had low GCS values/high SAPS1/high lactate
## - the other had high bilirubin/deranged LFTs/high lactate
## Decision: remove these outliers and re-fit the model to the dataset excluding these observations -->
# Check the RecordIDs match up with the correct data in the non-missing, split dataset
ICU.split[(ICU.split$RecordID == 136398 | ICU.split$RecordID == 137433),]## RecordID in_hospital_death Age Gender ICUType Weight_max Albumin_min
## 2512 136398 0 70 Female Medical ICU 78.2 3.0
## 2513 136398 0 70 Female Medical ICU 78.2 3.0
## 3226 137433 0 78 Male Medical ICU 76.0 2.3
## 3227 137433 0 78 Male Medical ICU 76.0 2.3
## Bilirubin_max BUN_max Creatinine_max GCS_max Glucose_min Glucose_max
## 2512 0.9 124 6.4 9 41 282
## 2513 0.9 124 6.4 9 41 282
## 3226 6.7 122 4.2 15 73 73
## 3227 6.7 122 4.2 15 73 73
## HCO3_min HR_min HR_max K_min K_max Lactate_max MAP_min Na_min Na_max
## 2512 7 42 70 3.5 3.9 7.6 55 131 133
## 2513 7 42 70 3.5 3.9 7.6 55 131 133
## 3226 22 60 65 4.0 4.0 5.0 65 133 133
## 3227 22 60 65 4.0 4.0 5.0 65 133 133
## Platelets_min PFratio pH_min pH_max RespRate_min RespRate_max Temp_min
## 2512 112 120 7.22 7.31 10 30 34.4
## 2513 112 120 7.22 7.31 10 30 34.4
## 3226 344 50 7.29 7.31 17 31 35.8
## 3227 344 50 7.29 7.31 17 31 35.8
## Temp_max TroponinT_max TroponinI_max Urine_min WBC_min WBC_max id2 tstart
## 2512 36.1 0.27 3.9 0 8.4 9.8 1400 0
## 2513 36.1 0.27 3.9 0 8.4 9.8 1400 90
## 3226 37.9 4.01 3.9 0 12.8 12.8 1792 0
## 3227 37.9 4.01 3.9 0 12.8 12.8 1792 90
## Days Status tgroup
## 2512 90 0 1
## 2513 2408 0 2
## 3226 90 0 1
## 3227 2408 0 2# Remove these observations and save as new dataset
ICU.split_noutliers <- ICU.split[!(ICU.split$RecordID %in% c(136398, 137433)),]
# Refit the split model to the new dataset
ICU.mv_reduced4.split.noutliers <- coxph(Surv(Days, Status) ~
Age + ICUType:strata(tgroup) +
Albumin_min:strata(tgroup) +
Bilirubin_max:strata(tgroup) + BUN_max +
GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
HR_min:strata(tgroup) +
Lactate_max:strata(tgroup) + Na_max + pH_min +
Temp_max + Urine_min,
data = ICU.split_noutliers)
summary(ICU.mv_reduced4.split.noutliers)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) +
## Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) +
## BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
## HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max +
## pH_min + Temp_max + Urine_min, data = ICU.split_noutliers)
##
## n= 3444, number of events= 721
##
## coef
## Age 0.0345124
## BUN_max 0.0111342
## Na_max -0.0404555
## pH_min -0.4124840
## Temp_max -0.1582918
## Urine_min -0.0019812
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.0221166
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1586329
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.2008633
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.0655282
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3071060
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5463547
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min -0.2312474
## strata(tgroup)tgroup=2:Albumin_min 0.0257121
## strata(tgroup)tgroup=1:Bilirubin_max 0.0287543
## strata(tgroup)tgroup=2:Bilirubin_max -0.0159728
## strata(tgroup)tgroup=1:GCS_max -0.1281817
## strata(tgroup)tgroup=2:GCS_max -0.0686489
## strata(tgroup)tgroup=1:HCO3_min -0.0033246
## strata(tgroup)tgroup=2:HCO3_min 0.0391071
## strata(tgroup)tgroup=1:HR_min 0.0081504
## strata(tgroup)tgroup=2:HR_min 0.0013052
## strata(tgroup)tgroup=1:Lactate_max 0.0904054
## strata(tgroup)tgroup=2:Lactate_max -0.0013510
## exp(coef)
## Age 1.0351149
## BUN_max 1.0111965
## Na_max 0.9603519
## pH_min 0.6620038
## Temp_max 0.8536006
## Urine_min 0.9980208
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0223630
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139150
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2224577
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677228
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7355726
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269462
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935431
## strata(tgroup)tgroup=2:Albumin_min 1.0260455
## strata(tgroup)tgroup=1:Bilirubin_max 1.0291717
## strata(tgroup)tgroup=2:Bilirubin_max 0.9841541
## strata(tgroup)tgroup=1:GCS_max 0.8796935
## strata(tgroup)tgroup=2:GCS_max 0.9336545
## strata(tgroup)tgroup=1:HCO3_min 0.9966809
## strata(tgroup)tgroup=2:HCO3_min 1.0398819
## strata(tgroup)tgroup=1:HR_min 1.0081837
## strata(tgroup)tgroup=2:HR_min 1.0013060
## strata(tgroup)tgroup=1:Lactate_max 1.0946180
## strata(tgroup)tgroup=2:Lactate_max 0.9986499
## se(coef) z
## Age 0.0027499 12.550
## BUN_max 0.0013776 8.082
## Na_max 0.0078816 -5.133
## pH_min 0.1978059 -2.085
## Temp_max 0.0521644 -3.034
## Urine_min 0.0009464 -2.093
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.1694156 0.131
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2047092 -5.660
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.1311915 1.531
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 0.0000000 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.1898951 0.345
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.1780033 -1.725
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.1496993 3.650
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 0.0000000 NA
## strata(tgroup)tgroup=1:Albumin_min 0.0875372 -2.642
## strata(tgroup)tgroup=2:Albumin_min 0.0932299 0.276
## strata(tgroup)tgroup=1:Bilirubin_max 0.0081724 3.518
## strata(tgroup)tgroup=2:Bilirubin_max 0.0173879 -0.919
## strata(tgroup)tgroup=1:GCS_max 0.0157330 -8.147
## strata(tgroup)tgroup=2:GCS_max 0.0190784 -3.598
## strata(tgroup)tgroup=1:HCO3_min 0.0117341 -0.283
## strata(tgroup)tgroup=2:HCO3_min 0.0123778 3.159
## strata(tgroup)tgroup=1:HR_min 0.0032554 2.504
## strata(tgroup)tgroup=2:HR_min 0.0038581 0.338
## strata(tgroup)tgroup=1:Lactate_max 0.0202818 4.457
## strata(tgroup)tgroup=2:Lactate_max 0.0342960 -0.039
## Pr(>|z|)
## Age < 0.0000000000000002
## BUN_max 0.000000000000000636
## Na_max 0.000000285293278950
## pH_min 0.037042
## Temp_max 0.002410
## Urine_min 0.036316
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.896134
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015146402643
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.125752
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.730037
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.084477
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.000263
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.008249
## strata(tgroup)tgroup=2:Albumin_min 0.782708
## strata(tgroup)tgroup=1:Bilirubin_max 0.000434
## strata(tgroup)tgroup=2:Bilirubin_max 0.358295
## strata(tgroup)tgroup=1:GCS_max 0.000000000000000372
## strata(tgroup)tgroup=2:GCS_max 0.000320
## strata(tgroup)tgroup=1:HCO3_min 0.776925
## strata(tgroup)tgroup=2:HCO3_min 0.001581
## strata(tgroup)tgroup=1:HR_min 0.012291
## strata(tgroup)tgroup=2:HR_min 0.735142
## strata(tgroup)tgroup=1:Lactate_max 0.000008293318325089
## strata(tgroup)tgroup=2:Lactate_max 0.968577
##
## Age ***
## BUN_max ***
## Na_max ***
## pH_min *
## Temp_max **
## Urine_min *
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
## ICUTypeMedical ICU:strata(tgroup)tgroup=1
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 ***
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2
## strata(tgroup)tgroup=1:Albumin_min **
## strata(tgroup)tgroup=2:Albumin_min
## strata(tgroup)tgroup=1:Bilirubin_max ***
## strata(tgroup)tgroup=2:Bilirubin_max
## strata(tgroup)tgroup=1:GCS_max ***
## strata(tgroup)tgroup=2:GCS_max ***
## strata(tgroup)tgroup=1:HCO3_min
## strata(tgroup)tgroup=2:HCO3_min **
## strata(tgroup)tgroup=1:HR_min *
## strata(tgroup)tgroup=2:HR_min
## strata(tgroup)tgroup=1:Lactate_max ***
## strata(tgroup)tgroup=2:Lactate_max
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef)
## Age 1.0351
## BUN_max 1.0112
## Na_max 0.9604
## pH_min 0.6620
## Temp_max 0.8536
## Urine_min 0.9980
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0224
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2225
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7356
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935
## strata(tgroup)tgroup=2:Albumin_min 1.0260
## strata(tgroup)tgroup=1:Bilirubin_max 1.0292
## strata(tgroup)tgroup=2:Bilirubin_max 0.9842
## strata(tgroup)tgroup=1:GCS_max 0.8797
## strata(tgroup)tgroup=2:GCS_max 0.9337
## strata(tgroup)tgroup=1:HCO3_min 0.9967
## strata(tgroup)tgroup=2:HCO3_min 1.0399
## strata(tgroup)tgroup=1:HR_min 1.0082
## strata(tgroup)tgroup=2:HR_min 1.0013
## strata(tgroup)tgroup=1:Lactate_max 1.0946
## strata(tgroup)tgroup=2:Lactate_max 0.9986
## exp(-coef)
## Age 0.9661
## BUN_max 0.9889
## Na_max 1.0413
## pH_min 1.5106
## Temp_max 1.1715
## Urine_min 1.0020
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.9781
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 3.1856
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.8180
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.9366
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.3595
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5791
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 1.2602
## strata(tgroup)tgroup=2:Albumin_min 0.9746
## strata(tgroup)tgroup=1:Bilirubin_max 0.9717
## strata(tgroup)tgroup=2:Bilirubin_max 1.0161
## strata(tgroup)tgroup=1:GCS_max 1.1368
## strata(tgroup)tgroup=2:GCS_max 1.0711
## strata(tgroup)tgroup=1:HCO3_min 1.0033
## strata(tgroup)tgroup=2:HCO3_min 0.9616
## strata(tgroup)tgroup=1:HR_min 0.9919
## strata(tgroup)tgroup=2:HR_min 0.9987
## strata(tgroup)tgroup=1:Lactate_max 0.9136
## strata(tgroup)tgroup=2:Lactate_max 1.0014
## lower .95 upper .95
## Age 1.0296 1.0407
## BUN_max 1.0085 1.0139
## Na_max 0.9456 0.9753
## pH_min 0.4492 0.9755
## Temp_max 0.7706 0.9455
## Urine_min 0.9962 0.9999
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.7335 1.4250
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2102 0.4689
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.9453 1.5809
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7359 1.5492
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.5189 1.0427
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.2878 2.3158
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA NA
## strata(tgroup)tgroup=1:Albumin_min 0.6684 0.9421
## strata(tgroup)tgroup=2:Albumin_min 0.8547 1.2318
## strata(tgroup)tgroup=1:Bilirubin_max 1.0128 1.0458
## strata(tgroup)tgroup=2:Bilirubin_max 0.9512 1.0183
## strata(tgroup)tgroup=1:GCS_max 0.8530 0.9072
## strata(tgroup)tgroup=2:GCS_max 0.8994 0.9692
## strata(tgroup)tgroup=1:HCO3_min 0.9740 1.0199
## strata(tgroup)tgroup=2:HCO3_min 1.0150 1.0654
## strata(tgroup)tgroup=1:HR_min 1.0018 1.0146
## strata(tgroup)tgroup=2:HR_min 0.9938 1.0089
## strata(tgroup)tgroup=1:Lactate_max 1.0520 1.1390
## strata(tgroup)tgroup=2:Lactate_max 0.9337 1.0681
##
## Concordance= 0.749 (se = 0.009 )
## Likelihood ratio test= 577.1 on 24 df, p=<0.0000000000000002
## Wald test = 558.2 on 24 df, p=<0.0000000000000002
## Score (logrank) test = 607.6 on 24 df, p=<0.0000000000000002# Calculate the split/no outlier model AIC
AIC.mv_reduced4.split.noutliers <- calc_aic(ICU.mv_reduced4.split.noutliers)
AIC.mv_reduced4.split.noutliers #10057 -- improvement## [1] 10057.49## Decision: use the 4th reduced model, split at time 3 months (90 days) on the split dataset with the outliers removed as the final dataset
# Difference in Coefficients
ICU.mv_reduced4.split.noutliers$coefficients## Age
## 0.034512415
## BUN_max
## 0.011134243
## Na_max
## -0.040455500
## pH_min
## -0.412483973
## Temp_max
## -0.158291825
## Urine_min
## -0.001981208
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1
## 0.022116637
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1
## -1.158632885
## ICUTypeMedical ICU:strata(tgroup)tgroup=1
## 0.200863301
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1
## NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2
## 0.065528200
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2
## -0.307105991
## ICUTypeMedical ICU:strata(tgroup)tgroup=2
## 0.546354668
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2
## NA
## strata(tgroup)tgroup=1:Albumin_min
## -0.231247368
## strata(tgroup)tgroup=2:Albumin_min
## 0.025712052
## strata(tgroup)tgroup=1:Bilirubin_max
## 0.028754332
## strata(tgroup)tgroup=2:Bilirubin_max
## -0.015972822
## strata(tgroup)tgroup=1:GCS_max
## -0.128181712
## strata(tgroup)tgroup=2:GCS_max
## -0.068648865
## strata(tgroup)tgroup=1:HCO3_min
## -0.003324595
## strata(tgroup)tgroup=2:HCO3_min
## 0.039107123
## strata(tgroup)tgroup=1:HR_min
## 0.008150402
## strata(tgroup)tgroup=2:HR_min
## 0.001305155
## strata(tgroup)tgroup=1:Lactate_max
## 0.090405433
## strata(tgroup)tgroup=2:Lactate_max
## -0.001351005ICU.mv_reduced4$coefficients## Age ICUTypeCardiac Surgery Recovery Unit
## 0.035038790 -0.750679504
## ICUTypeMedical ICU ICUTypeSurgical ICU
## 0.296653600 -0.048997022
## Albumin_min Bilirubin_max
## -0.097502837 0.017685740
## BUN_max GCS_max
## 0.010354185 -0.102515243
## HCO3_min HR_min
## 0.016951994 0.006489375
## Lactate_max Na_max
## 0.056092701 -0.036275765
## pH_min Temp_max
## -0.468490974 -0.153788543
## Urine_min
## -0.001949602We need to test whether the chosen model satisfies the assumptions underlying the Cox Proportional Hazards model.
- Testing for proportional hazards assumption
Proportional hazard assumption is supported by a non-significant relationship between residuals and time, while a significant relationship favours the null of non-constant hazards.
The output from the proportional hazards test shows that the test is statistically significant (p-value < 0.05) for
ICUType,Albumin_min,Bilirubin_max,GCS_max,HCO3_min,HR_minandLactate_max. The global test is also statistically significant (p-value is very small = 1.0e-12). Therefore, there appears to be a violation of the proportional hazards model.We choose to address the violations of the proportional hazards assumption by including time x covariate interactions in the model for the variables that violated the proportional hazards assumption. By looking at the survival curve and the asusmption that there may be systematic differences in patients who survive less than or greater than 3 months after ICU admission, we choose a post ICU survival time of 90 days.
The hazard rate increases at varying rates for the population who survived less than 90 days. add inferences for coefficients, CI’s and hazard rates
Allowing the regression coefficients to differ in the two time intervals (before 90 days and after) has helped address the violation of the PH assumption. The global test for our model is no longer significant (p-value =0.07).
- Check linearity by observing Martingale residuals for continuous variables
- We observe a close to linear relationship for
Age,Albumin_min,Bilirubin_max,GCS_max,Lactate_maxandUrine_minvariables. - There is a clear ly non-linear relationship for
BUN_max,HCO3_min,HR_min,Na-max,pH_minandTemp_max. - Explanation - especially with laboratory values very far from the reference ranges (likely few observations in this range / potential outliers) Can someone explain this a bit better?
- Checking linearity for the model as a whole
The overall model residuals appear reasonably linear around 0. However, we do observe 2 very large negative outliers (individuals whose actual survival time was significantly greater than estimated by the model. On closer observation, these 2 individuals were relatively elderly with long lengths of stay in hospital. One had low GCS values, high SAPS1, high lactate whilst the other had high bilirubin, deranged LFTs and high lactate, all indicators of high risk of mortality.
We have removed these outliers observations and re-fit the model to the dataset excluding these observations. The model fit has improved (with AIC now 10,057 compared to 10,112). The resulting changes in coefficients include: add comparison to previous inferences on coefficients, CI’s and hazard rates
Final multivariable Cox proportional hazards model:
ICU.final.cox <- coxph(Surv(Days, Status) ~
Age + ICUType:strata(tgroup) +
Albumin_min:strata(tgroup) +
Bilirubin_max:strata(tgroup) + BUN_max +
GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
HR_min:strata(tgroup) + Lactate_max:strata(tgroup) +
Na_max + pH_min + Temp_max + Urine_min,
data = ICU.split_noutliers)
summary(ICU.final.cox)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) +
## Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) +
## BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
## HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max +
## pH_min + Temp_max + Urine_min, data = ICU.split_noutliers)
##
## n= 3444, number of events= 721
##
## coef
## Age 0.0345124
## BUN_max 0.0111342
## Na_max -0.0404555
## pH_min -0.4124840
## Temp_max -0.1582918
## Urine_min -0.0019812
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.0221166
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1586329
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.2008633
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.0655282
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3071060
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5463547
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min -0.2312474
## strata(tgroup)tgroup=2:Albumin_min 0.0257121
## strata(tgroup)tgroup=1:Bilirubin_max 0.0287543
## strata(tgroup)tgroup=2:Bilirubin_max -0.0159728
## strata(tgroup)tgroup=1:GCS_max -0.1281817
## strata(tgroup)tgroup=2:GCS_max -0.0686489
## strata(tgroup)tgroup=1:HCO3_min -0.0033246
## strata(tgroup)tgroup=2:HCO3_min 0.0391071
## strata(tgroup)tgroup=1:HR_min 0.0081504
## strata(tgroup)tgroup=2:HR_min 0.0013052
## strata(tgroup)tgroup=1:Lactate_max 0.0904054
## strata(tgroup)tgroup=2:Lactate_max -0.0013510
## exp(coef)
## Age 1.0351149
## BUN_max 1.0111965
## Na_max 0.9603519
## pH_min 0.6620038
## Temp_max 0.8536006
## Urine_min 0.9980208
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0223630
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139150
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2224577
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677228
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7355726
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269462
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935431
## strata(tgroup)tgroup=2:Albumin_min 1.0260455
## strata(tgroup)tgroup=1:Bilirubin_max 1.0291717
## strata(tgroup)tgroup=2:Bilirubin_max 0.9841541
## strata(tgroup)tgroup=1:GCS_max 0.8796935
## strata(tgroup)tgroup=2:GCS_max 0.9336545
## strata(tgroup)tgroup=1:HCO3_min 0.9966809
## strata(tgroup)tgroup=2:HCO3_min 1.0398819
## strata(tgroup)tgroup=1:HR_min 1.0081837
## strata(tgroup)tgroup=2:HR_min 1.0013060
## strata(tgroup)tgroup=1:Lactate_max 1.0946180
## strata(tgroup)tgroup=2:Lactate_max 0.9986499
## se(coef) z
## Age 0.0027499 12.550
## BUN_max 0.0013776 8.082
## Na_max 0.0078816 -5.133
## pH_min 0.1978059 -2.085
## Temp_max 0.0521644 -3.034
## Urine_min 0.0009464 -2.093
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.1694156 0.131
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2047092 -5.660
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.1311915 1.531
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 0.0000000 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.1898951 0.345
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.1780033 -1.725
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.1496993 3.650
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 0.0000000 NA
## strata(tgroup)tgroup=1:Albumin_min 0.0875372 -2.642
## strata(tgroup)tgroup=2:Albumin_min 0.0932299 0.276
## strata(tgroup)tgroup=1:Bilirubin_max 0.0081724 3.518
## strata(tgroup)tgroup=2:Bilirubin_max 0.0173879 -0.919
## strata(tgroup)tgroup=1:GCS_max 0.0157330 -8.147
## strata(tgroup)tgroup=2:GCS_max 0.0190784 -3.598
## strata(tgroup)tgroup=1:HCO3_min 0.0117341 -0.283
## strata(tgroup)tgroup=2:HCO3_min 0.0123778 3.159
## strata(tgroup)tgroup=1:HR_min 0.0032554 2.504
## strata(tgroup)tgroup=2:HR_min 0.0038581 0.338
## strata(tgroup)tgroup=1:Lactate_max 0.0202818 4.457
## strata(tgroup)tgroup=2:Lactate_max 0.0342960 -0.039
## Pr(>|z|)
## Age < 0.0000000000000002
## BUN_max 0.000000000000000636
## Na_max 0.000000285293278950
## pH_min 0.037042
## Temp_max 0.002410
## Urine_min 0.036316
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.896134
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015146402643
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.125752
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.730037
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.084477
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.000263
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.008249
## strata(tgroup)tgroup=2:Albumin_min 0.782708
## strata(tgroup)tgroup=1:Bilirubin_max 0.000434
## strata(tgroup)tgroup=2:Bilirubin_max 0.358295
## strata(tgroup)tgroup=1:GCS_max 0.000000000000000372
## strata(tgroup)tgroup=2:GCS_max 0.000320
## strata(tgroup)tgroup=1:HCO3_min 0.776925
## strata(tgroup)tgroup=2:HCO3_min 0.001581
## strata(tgroup)tgroup=1:HR_min 0.012291
## strata(tgroup)tgroup=2:HR_min 0.735142
## strata(tgroup)tgroup=1:Lactate_max 0.000008293318325089
## strata(tgroup)tgroup=2:Lactate_max 0.968577
##
## Age ***
## BUN_max ***
## Na_max ***
## pH_min *
## Temp_max **
## Urine_min *
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
## ICUTypeMedical ICU:strata(tgroup)tgroup=1
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 ***
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2
## strata(tgroup)tgroup=1:Albumin_min **
## strata(tgroup)tgroup=2:Albumin_min
## strata(tgroup)tgroup=1:Bilirubin_max ***
## strata(tgroup)tgroup=2:Bilirubin_max
## strata(tgroup)tgroup=1:GCS_max ***
## strata(tgroup)tgroup=2:GCS_max ***
## strata(tgroup)tgroup=1:HCO3_min
## strata(tgroup)tgroup=2:HCO3_min **
## strata(tgroup)tgroup=1:HR_min *
## strata(tgroup)tgroup=2:HR_min
## strata(tgroup)tgroup=1:Lactate_max ***
## strata(tgroup)tgroup=2:Lactate_max
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef)
## Age 1.0351
## BUN_max 1.0112
## Na_max 0.9604
## pH_min 0.6620
## Temp_max 0.8536
## Urine_min 0.9980
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0224
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2225
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7356
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935
## strata(tgroup)tgroup=2:Albumin_min 1.0260
## strata(tgroup)tgroup=1:Bilirubin_max 1.0292
## strata(tgroup)tgroup=2:Bilirubin_max 0.9842
## strata(tgroup)tgroup=1:GCS_max 0.8797
## strata(tgroup)tgroup=2:GCS_max 0.9337
## strata(tgroup)tgroup=1:HCO3_min 0.9967
## strata(tgroup)tgroup=2:HCO3_min 1.0399
## strata(tgroup)tgroup=1:HR_min 1.0082
## strata(tgroup)tgroup=2:HR_min 1.0013
## strata(tgroup)tgroup=1:Lactate_max 1.0946
## strata(tgroup)tgroup=2:Lactate_max 0.9986
## exp(-coef)
## Age 0.9661
## BUN_max 0.9889
## Na_max 1.0413
## pH_min 1.5106
## Temp_max 1.1715
## Urine_min 1.0020
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.9781
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 3.1856
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.8180
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.9366
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.3595
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5791
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 1.2602
## strata(tgroup)tgroup=2:Albumin_min 0.9746
## strata(tgroup)tgroup=1:Bilirubin_max 0.9717
## strata(tgroup)tgroup=2:Bilirubin_max 1.0161
## strata(tgroup)tgroup=1:GCS_max 1.1368
## strata(tgroup)tgroup=2:GCS_max 1.0711
## strata(tgroup)tgroup=1:HCO3_min 1.0033
## strata(tgroup)tgroup=2:HCO3_min 0.9616
## strata(tgroup)tgroup=1:HR_min 0.9919
## strata(tgroup)tgroup=2:HR_min 0.9987
## strata(tgroup)tgroup=1:Lactate_max 0.9136
## strata(tgroup)tgroup=2:Lactate_max 1.0014
## lower .95 upper .95
## Age 1.0296 1.0407
## BUN_max 1.0085 1.0139
## Na_max 0.9456 0.9753
## pH_min 0.4492 0.9755
## Temp_max 0.7706 0.9455
## Urine_min 0.9962 0.9999
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.7335 1.4250
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2102 0.4689
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.9453 1.5809
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7359 1.5492
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.5189 1.0427
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.2878 2.3158
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA NA
## strata(tgroup)tgroup=1:Albumin_min 0.6684 0.9421
## strata(tgroup)tgroup=2:Albumin_min 0.8547 1.2318
## strata(tgroup)tgroup=1:Bilirubin_max 1.0128 1.0458
## strata(tgroup)tgroup=2:Bilirubin_max 0.9512 1.0183
## strata(tgroup)tgroup=1:GCS_max 0.8530 0.9072
## strata(tgroup)tgroup=2:GCS_max 0.8994 0.9692
## strata(tgroup)tgroup=1:HCO3_min 0.9740 1.0199
## strata(tgroup)tgroup=2:HCO3_min 1.0150 1.0654
## strata(tgroup)tgroup=1:HR_min 1.0018 1.0146
## strata(tgroup)tgroup=2:HR_min 0.9938 1.0089
## strata(tgroup)tgroup=1:Lactate_max 1.0520 1.1390
## strata(tgroup)tgroup=2:Lactate_max 0.9337 1.0681
##
## Concordance= 0.749 (se = 0.009 )
## Likelihood ratio test= 577.1 on 24 df, p=<0.0000000000000002
## Wald test = 558.2 on 24 df, p=<0.0000000000000002
## Score (logrank) test = 607.6 on 24 df, p=<0.0000000000000002Final model diagnostics:
# PH test
cox.zph(ICU.final.cox, terms=FALSE)## chisq df p
## Age 0.141243 1 0.7070
## BUN_max 0.175156 1 0.6756
## Na_max 0.456307 1 0.4994
## pH_min 0.198734 1 0.6557
## Temp_max 0.408536 1 0.5227
## Urine_min 1.609218 1 0.2046
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.005054 1 0.9433
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.638643 1 0.4242
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.000111 1 0.9916
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.123591 1 0.7252
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 2.076903 1 0.1495
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.548959 1 0.4587
## strata(tgroup)tgroup=1:Albumin_min 2.240730 1 0.1344
## strata(tgroup)tgroup=2:Albumin_min 0.001434 1 0.9698
## strata(tgroup)tgroup=1:Bilirubin_max 0.849315 1 0.3567
## strata(tgroup)tgroup=2:Bilirubin_max 3.264521 1 0.0708
## strata(tgroup)tgroup=1:GCS_max 10.385598 1 0.0013
## strata(tgroup)tgroup=2:GCS_max 2.498280 1 0.1140
## strata(tgroup)tgroup=1:HCO3_min 4.521139 1 0.0335
## strata(tgroup)tgroup=2:HCO3_min 1.519178 1 0.2177
## strata(tgroup)tgroup=1:HR_min 1.125927 1 0.2886
## strata(tgroup)tgroup=2:HR_min 0.356000 1 0.5507
## strata(tgroup)tgroup=1:Lactate_max 4.188790 1 0.0407
## strata(tgroup)tgroup=2:Lactate_max 5.769251 1 0.0163
## GLOBAL 34.296951 24 0.0795# Graph of Schoenfeld residuals
#ggcoxzph(cox.zph(ICU.final.cox, terms=FALSE))
ggcoxdiagnostics(ICU.final.cox, type = "schoenfeld", title = "Diagnostic plot")## `geom_smooth()` using formula 'y ~ x'
Final Model Diagnostics:
- Proportional Hazards Assumptions
Proportional hazard assumption is supported by a non-significant relationship between residuals and time, while a significant relationship favours the null of non-constant hazards. The global test on the final model is not statistically significant (p-value is 0.08). Therefore, there does not appear to be a violation of the proportional hazards assumption.
The output from the proportional hazards test shows that the test is statistically significant at a 5% significance level for
GCS_max,HCO3_min, andLactate_max, though improved from before incorporating time x covariate split.
- Schoenfeld Residuals
The Schoenfeld residuals represent the difference between the observed covariates and expected value for the individuals who failed (i.e. did not survive). In the graphs of the scaled Schoenfeld residuals, the blue dotted line is a smoothing spline fit to the residuals (black dots), with the dashed red line representing the zero line. Systematic departures from the red horizontal line are indicative of non-proportional hazards, since proportional hazards assumes that estimates do not vary much over time. Graphical inspection does not show systematic departures from the zero line over time.
Re-fitting the model to the original data:
##Compare model on df0 to df1
nm_icu_model_df0 <- na.omit(subset(icu_patients_df0,
select=c(Days, Status, # the survival object variables
RecordID, # keep record id for reference if needed
Age, ICUType,
Albumin_min, Bilirubin_max, BUN_max, GCS_max, HCO3_min, HR_min, Lactate_max, Na_max, pH_min,
Temp_max, Urine_min)))
dim(nm_icu_model_df0)## [1] 299 16ICUdf0.split <- survSplit(Surv(Days, Status) ~ ., data = nm_icu_model_df0, cut=c(90), episode= "tgroup", id="id2")
head(icu_patients_df0)## RecordID Length_of_stay SAPS1 SOFA Survival in_hospital_death Days Status Age
## 1 132539 5 6 1 NA 0 2408 FALSE 54
## 2 132540 8 16 8 NA 0 2408 FALSE 76
## 3 132541 19 21 11 NA 0 2408 FALSE 44
## 4 132543 9 7 1 575 0 575 TRUE 68
## 5 132545 4 17 2 918 0 918 TRUE 88
## 6 132547 6 14 11 1637 0 1637 TRUE 64
## Albumin_diff Albumin_max Albumin_min ALP_diff ALP_max ALP_min ALT_diff
## 1 NA NA NA NA NA NA NA
## 2 NA NA NA NA NA NA NA
## 3 0.6813367 2.7 2.3 31.147964 127 105 45.44617
## 4 1.4186633 4.4 4.4 9.147964 105 105 108.44617
## 5 NA NA NA NA NA NA NA
## 6 NA NA NA 5.147964 101 101 75.44617
## ALT_max ALT_min AST_diff AST_max AST_min Bilirubin_diff Bilirubin_max
## 1 NA NA NA NA NA NA NA
## 2 NA NA NA NA NA NA NA
## 3 91 75 65.64729 235 164 1.235961 3.0
## 4 12 12 154.35271 15 15 1.564039 0.2
## 5 NA NA NA NA NA NA NA
## 6 60 45 122.35271 162 47 1.364039 0.4
## Bilirubin_min BUN_diff BUN_max BUN_min Cholesterol_diff Cholesterol_max
## 1 NA 11.527053 13 13 NA NA
## 2 NA 8.527053 18 16 NA NA
## 3 2.8 21.527053 8 3 NA NA
## 4 0.2 4.527053 23 20 NA NA
## 5 NA 20.472947 45 45 NA NA
## 6 0.4 9.527053 19 15 55.57724 212
## Cholesterol_min Creatinine_diff Creatinine_max Creatinine_min DiasABP_diff
## 1 NA 0.4324463 0.8 0.8 NA
## 2 NA 0.4324463 1.2 0.8 26.54421
## 3 NA 0.9324463 0.4 0.3 NA
## 4 NA 0.5324463 0.9 0.7 NA
## 5 NA 0.2324463 1.0 1.0 NA
## 6 212 0.3324463 1.4 0.9 20.45579
## DiasABP_max DiasABP_min FiO2_diff FiO2_max FiO2_min GCS_diff GCS_max GCS_min
## 1 NA NA NA NA NA 3.755971 15 15
## 2 81 32 0.44807988 1.0 0.4 8.244029 15 3
## 3 NA NA 0.44807988 1.0 0.5 6.244029 8 5
## 4 NA NA NA NA NA 3.755971 15 14
## 5 NA NA NA NA NA 3.755971 15 15
## 6 79 55 0.05192012 0.5 0.5 4.244029 9 7
## Gender Glucose_diff Glucose_max Glucose_min HCO3_diff HCO3_max HCO3_min
## 1 Female 65.14446 205 205 3.227452 26 26
## 2 Male 34.85554 105 105 1.772548 22 21
## 3 Female 20.85554 141 119 3.227452 26 24
## 4 Male 33.85554 129 106 5.227452 28 27
## 5 Female 26.85554 113 113 4.772548 18 18
## 6 Male 124.14446 264 197 3.772548 19 19
## HCT_diff HCT_max HCT_min Height HR_diff HR_max HR_min
## 1 2.739871 33.7 33.5 -Inf 29.077891 80 58
## 2 6.260129 29.7 24.7 175.3 7.077891 88 80
## 3 4.260129 28.5 26.7 -Inf 30.077891 113 57
## 4 10.339871 41.3 36.1 180.3 30.077891 88 57
## 5 8.360129 30.8 22.6 -Inf 20.077891 94 67
## 6 10.639871 41.6 36.8 180.3 16.077891 91 71
## ICUType K_diff K_max K_min Lactate_diff Lactate_max
## 1 Surgical ICU 0.2647934 4.4 4.4 NA NA
## 2 Cardiac Surgery Recovery Unit 0.1647934 4.3 4.3 NA NA
## 3 Medical ICU 4.4647934 8.6 3.3 1.496404 1.9
## 4 Medical ICU 0.1352066 4.2 4.0 NA NA
## 5 Medical ICU 1.8647934 6.0 3.8 NA NA
## 6 Coronary Care Unit 0.9647934 5.1 3.8 NA NA
## Lactate_min MAP_diff MAP_max MAP_min Mg_diff Mg_max Mg_min Na_diff Na_max
## 1 NA NA NA NA 0.4842982 1.5 1.5 2.2066071 137
## 2 NA 34.76836 100 43 1.1157018 3.1 1.9 0.2066071 139
## 3 1.3 NA NA NA 0.6842982 1.9 1.3 2.2066071 140
## 4 NA NA NA NA 0.1157018 2.1 2.1 1.7933929 141
## 5 NA NA NA NA 0.4842982 1.5 1.5 0.7933929 140
## 6 NA 24.23164 102 62 0.2842982 1.7 1.7 2.2066071 141
## Na_min NIDiasABP_diff NIDiasABP_max NIDiasABP_min NIMAP_diff NIMAP_max
## 1 137 17.49101 65 40 17.04069 92.33
## 2 139 19.49101 65 38 26.38069 86.33
## 3 137 37.50899 95 66 34.28931 110.00
## 4 140 23.50899 81 54 24.98931 100.70
## 5 140 38.50899 96 29 29.98931 105.70
## 6 137 31.50899 89 52 26.58931 102.30
## NIMAP_min NISysABP_diff NISysABP_max NISysABP_min PaCO2_diff PaCO2_max
## 1 58.67 40.30125 157 96 NA NA
## 2 49.33 44.69875 129 72 7.335797 41
## 3 83.33 33.30125 150 111 3.335797 37
## 4 73.00 23.30125 140 102 NA NA
## 5 63.67 39.30125 156 119 NA NA
## 6 61.67 35.69875 129 81 5.335797 45
## PaCO2_min PaO2_diff PaO2_max PaO2_min pH_diff pH_max pH_min Platelets_diff
## 1 NA NA NA NA NA NA NA 31.23069
## 2 33 286.38211 445 89 0.08011376 7.45 7.34 36.23069
## 3 37 93.61789 65 65 0.14011376 7.51 7.51 117.76931
## 4 NA NA NA NA NA NA NA 201.23069
## 5 NA NA NA NA NA NA NA 80.76931
## 6 35 80.61789 101 78 0.07988624 7.40 7.29 86.23069
## Platelets_max Platelets_min RespRate_diff RespRate_max RespRate_min SaO2_diff
## 1 221 221 7.34858 24 12 NA
## 2 226 164 NA NA NA 1.753921
## 3 84 72 NA NA NA 2.246079
## 4 391 315 7.34858 21 12 NA
## 5 109 109 6.65142 26 15 NA
## 6 276 219 NA NA NA 1.246079
## SaO2_max SaO2_min SysABP_diff SysABP_max SysABP_min Temp_diff Temp_max
## 1 NA NA NA NA NA 1.874083 38.1
## 2 99 97 50.3105 135 66 2.474083 37.9
## 3 95 95 NA NA NA 2.025917 39.0
## 4 NA NA NA NA NA 1.874083 36.7
## 5 NA NA NA NA NA 1.174083 37.8
## 6 97 96 43.3105 152 73 1.174083 37.8
## Temp_min TroponinI_diff TroponinI_max TroponinI_min TroponinT_diff
## 1 35.1 NA NA NA NA
## 2 34.5 NA NA NA NA
## 3 36.7 NA NA NA NA
## 4 35.1 NA NA NA NA
## 5 35.8 NA NA NA NA
## 6 35.8 4.142945 1.3 1.3 NA
## TroponinT_max TroponinT_min Urine_diff Urine_max Urine_min WBC_diff WBC_max
## 1 NA NA 800.78242 900 30 0.9331524 11.2
## 2 NA NA 670.78242 770 0 4.7331524 13.1
## 3 NA NA 310.78242 410 30 8.4331524 4.2
## 4 NA NA 600.78242 700 100 3.3331524 11.5
## 5 NA NA 83.21758 150 16 8.3331524 3.8
## 6 NA NA 1100.78242 1200 40 11.8668476 24.0
## WBC_min Weight_diff Weight_max Weight_min PFratio
## 1 11.2 Inf -Inf Inf NA
## 2 7.4 4.699878 80.6 76.0 89
## 3 3.7 23.999878 56.7 56.7 65
## 4 8.8 3.900122 84.6 84.6 NA
## 5 3.8 Inf -Inf Inf NA
## 6 14.4 33.300122 114.0 114.0 156ICU.final.coxdf0 <- coxph(Surv(Days, Status) ~
Age + ICUType:strata(tgroup) +
Albumin_min:strata(tgroup) +
Bilirubin_max:strata(tgroup) + BUN_max +
GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
HR_min:strata(tgroup) + Lactate_max:strata(tgroup) +
Na_max + pH_min + Temp_max + Urine_min,
data = ICUdf0.split)
summary(ICU.final.coxdf0)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) +
## Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) +
## BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
## HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max +
## pH_min + Temp_max + Urine_min, data = ICUdf0.split)
##
## n= 521, number of events= 123
##
## coef
## Age 0.0308044
## BUN_max 0.0100748
## Na_max -0.0292607
## pH_min -1.9164019
## Temp_max 0.0199181
## Urine_min 0.0005413
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.4507477
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -2.4418221
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.4491899
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 -0.3107640
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.3418326
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.7695124
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min -0.4813815
## strata(tgroup)tgroup=2:Albumin_min -0.5003112
## strata(tgroup)tgroup=1:Bilirubin_max 0.0396806
## strata(tgroup)tgroup=2:Bilirubin_max 0.0404057
## strata(tgroup)tgroup=1:GCS_max -0.0875339
## strata(tgroup)tgroup=2:GCS_max 0.0024367
## strata(tgroup)tgroup=1:HCO3_min 0.0131254
## strata(tgroup)tgroup=2:HCO3_min 0.0986484
## strata(tgroup)tgroup=1:HR_min 0.0093436
## strata(tgroup)tgroup=2:HR_min -0.0102991
## strata(tgroup)tgroup=1:Lactate_max 0.0666912
## strata(tgroup)tgroup=2:Lactate_max -0.0140842
## exp(coef)
## Age 1.0312838
## BUN_max 1.0101257
## Na_max 0.9711633
## pH_min 0.1471354
## Temp_max 1.0201178
## Urine_min 1.0005414
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.5694852
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.0870022
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.5670422
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7328868
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.4075247
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 2.1587134
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.6179291
## strata(tgroup)tgroup=2:Albumin_min 0.6063419
## strata(tgroup)tgroup=1:Bilirubin_max 1.0404784
## strata(tgroup)tgroup=2:Bilirubin_max 1.0412331
## strata(tgroup)tgroup=1:GCS_max 0.9161878
## strata(tgroup)tgroup=2:GCS_max 1.0024397
## strata(tgroup)tgroup=1:HCO3_min 1.0132119
## strata(tgroup)tgroup=2:HCO3_min 1.1036782
## strata(tgroup)tgroup=1:HR_min 1.0093873
## strata(tgroup)tgroup=2:HR_min 0.9897538
## strata(tgroup)tgroup=1:Lactate_max 1.0689654
## strata(tgroup)tgroup=2:Lactate_max 0.9860145
## se(coef) z
## Age 0.0062516 4.927
## BUN_max 0.0028836 3.494
## Na_max 0.0203191 -1.440
## pH_min 0.9990481 -1.918
## Temp_max 0.1206279 0.165
## Urine_min 0.0032598 0.166
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.4818259 0.935
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 1.0372018 -2.354
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.2896715 1.551
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 0.0000000 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.8194792 -0.379
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.5020358 0.681
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.4141223 1.858
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 0.0000000 NA
## strata(tgroup)tgroup=1:Albumin_min 0.2051333 -2.347
## strata(tgroup)tgroup=2:Albumin_min 0.2791597 -1.792
## strata(tgroup)tgroup=1:Bilirubin_max 0.0177289 2.238
## strata(tgroup)tgroup=2:Bilirubin_max 0.0400231 1.010
## strata(tgroup)tgroup=1:GCS_max 0.0348508 -2.512
## strata(tgroup)tgroup=2:GCS_max 0.0474839 0.051
## strata(tgroup)tgroup=1:HCO3_min 0.0246870 0.532
## strata(tgroup)tgroup=2:HCO3_min 0.0294466 3.350
## strata(tgroup)tgroup=1:HR_min 0.0076902 1.215
## strata(tgroup)tgroup=2:HR_min 0.0112699 -0.914
## strata(tgroup)tgroup=1:Lactate_max 0.0444354 1.501
## strata(tgroup)tgroup=2:Lactate_max 0.0747284 -0.188
## Pr(>|z|)
## Age 0.000000833 ***
## BUN_max 0.000476 ***
## Na_max 0.149851
## pH_min 0.055082 .
## Temp_max 0.868849
## Urine_min 0.868123
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.349531
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.018561 *
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.120977
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.704524
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.495939
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.063144 .
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.018942 *
## strata(tgroup)tgroup=2:Albumin_min 0.073100 .
## strata(tgroup)tgroup=1:Bilirubin_max 0.025209 *
## strata(tgroup)tgroup=2:Bilirubin_max 0.312706
## strata(tgroup)tgroup=1:GCS_max 0.012016 *
## strata(tgroup)tgroup=2:GCS_max 0.959074
## strata(tgroup)tgroup=1:HCO3_min 0.594952
## strata(tgroup)tgroup=2:HCO3_min 0.000808 ***
## strata(tgroup)tgroup=1:HR_min 0.224367
## strata(tgroup)tgroup=2:HR_min 0.360793
## strata(tgroup)tgroup=1:Lactate_max 0.133392
## strata(tgroup)tgroup=2:Lactate_max 0.850507
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef)
## Age 1.0313
## BUN_max 1.0101
## Na_max 0.9712
## pH_min 0.1471
## Temp_max 1.0201
## Urine_min 1.0005
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.5695
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.0870
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.5670
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7329
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.4075
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 2.1587
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.6179
## strata(tgroup)tgroup=2:Albumin_min 0.6063
## strata(tgroup)tgroup=1:Bilirubin_max 1.0405
## strata(tgroup)tgroup=2:Bilirubin_max 1.0412
## strata(tgroup)tgroup=1:GCS_max 0.9162
## strata(tgroup)tgroup=2:GCS_max 1.0024
## strata(tgroup)tgroup=1:HCO3_min 1.0132
## strata(tgroup)tgroup=2:HCO3_min 1.1037
## strata(tgroup)tgroup=1:HR_min 1.0094
## strata(tgroup)tgroup=2:HR_min 0.9898
## strata(tgroup)tgroup=1:Lactate_max 1.0690
## strata(tgroup)tgroup=2:Lactate_max 0.9860
## exp(-coef)
## Age 0.9697
## BUN_max 0.9900
## Na_max 1.0297
## pH_min 6.7965
## Temp_max 0.9803
## Urine_min 0.9995
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.6372
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 11.4940
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.6381
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.3645
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7105
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.4632
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 1.6183
## strata(tgroup)tgroup=2:Albumin_min 1.6492
## strata(tgroup)tgroup=1:Bilirubin_max 0.9611
## strata(tgroup)tgroup=2:Bilirubin_max 0.9604
## strata(tgroup)tgroup=1:GCS_max 1.0915
## strata(tgroup)tgroup=2:GCS_max 0.9976
## strata(tgroup)tgroup=1:HCO3_min 0.9870
## strata(tgroup)tgroup=2:HCO3_min 0.9061
## strata(tgroup)tgroup=1:HR_min 0.9907
## strata(tgroup)tgroup=2:HR_min 1.0104
## strata(tgroup)tgroup=1:Lactate_max 0.9355
## strata(tgroup)tgroup=2:Lactate_max 1.0142
## lower .95 upper .95
## Age 1.01872 1.0440
## BUN_max 1.00443 1.0159
## Na_max 0.93325 1.0106
## pH_min 0.02076 1.0426
## Temp_max 0.80533 1.2922
## Urine_min 0.99417 1.0070
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.61042 4.0354
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.01139 0.6644
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.88820 2.7647
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.14706 3.6524
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.52617 3.7652
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.95872 4.8607
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA NA
## strata(tgroup)tgroup=1:Albumin_min 0.41336 0.9237
## strata(tgroup)tgroup=2:Albumin_min 0.35083 1.0479
## strata(tgroup)tgroup=1:Bilirubin_max 1.00494 1.0773
## strata(tgroup)tgroup=2:Bilirubin_max 0.96268 1.1262
## strata(tgroup)tgroup=1:GCS_max 0.85570 0.9810
## strata(tgroup)tgroup=2:GCS_max 0.91336 1.1002
## strata(tgroup)tgroup=1:HCO3_min 0.96535 1.0634
## strata(tgroup)tgroup=2:HCO3_min 1.04178 1.1693
## strata(tgroup)tgroup=1:HR_min 0.99429 1.0247
## strata(tgroup)tgroup=2:HR_min 0.96813 1.0119
## strata(tgroup)tgroup=1:Lactate_max 0.97981 1.1662
## strata(tgroup)tgroup=2:Lactate_max 0.85168 1.1415
##
## Concordance= 0.756 (se = 0.021 )
## Likelihood ratio test= 106.4 on 24 df, p=0.000000000002
## Wald test = 94.65 on 24 df, p=0.0000000002
## Score (logrank) test = 104.6 on 24 df, p=0.000000000005summary(ICU.final.cox)## Call:
## coxph(formula = Surv(Days, Status) ~ Age + ICUType:strata(tgroup) +
## Albumin_min:strata(tgroup) + Bilirubin_max:strata(tgroup) +
## BUN_max + GCS_max:strata(tgroup) + HCO3_min:strata(tgroup) +
## HR_min:strata(tgroup) + Lactate_max:strata(tgroup) + Na_max +
## pH_min + Temp_max + Urine_min, data = ICU.split_noutliers)
##
## n= 3444, number of events= 721
##
## coef
## Age 0.0345124
## BUN_max 0.0111342
## Na_max -0.0404555
## pH_min -0.4124840
## Temp_max -0.1582918
## Urine_min -0.0019812
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.0221166
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 -1.1586329
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.2008633
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.0655282
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 -0.3071060
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5463547
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min -0.2312474
## strata(tgroup)tgroup=2:Albumin_min 0.0257121
## strata(tgroup)tgroup=1:Bilirubin_max 0.0287543
## strata(tgroup)tgroup=2:Bilirubin_max -0.0159728
## strata(tgroup)tgroup=1:GCS_max -0.1281817
## strata(tgroup)tgroup=2:GCS_max -0.0686489
## strata(tgroup)tgroup=1:HCO3_min -0.0033246
## strata(tgroup)tgroup=2:HCO3_min 0.0391071
## strata(tgroup)tgroup=1:HR_min 0.0081504
## strata(tgroup)tgroup=2:HR_min 0.0013052
## strata(tgroup)tgroup=1:Lactate_max 0.0904054
## strata(tgroup)tgroup=2:Lactate_max -0.0013510
## exp(coef)
## Age 1.0351149
## BUN_max 1.0111965
## Na_max 0.9603519
## pH_min 0.6620038
## Temp_max 0.8536006
## Urine_min 0.9980208
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0223630
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139150
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2224577
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677228
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7355726
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269462
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935431
## strata(tgroup)tgroup=2:Albumin_min 1.0260455
## strata(tgroup)tgroup=1:Bilirubin_max 1.0291717
## strata(tgroup)tgroup=2:Bilirubin_max 0.9841541
## strata(tgroup)tgroup=1:GCS_max 0.8796935
## strata(tgroup)tgroup=2:GCS_max 0.9336545
## strata(tgroup)tgroup=1:HCO3_min 0.9966809
## strata(tgroup)tgroup=2:HCO3_min 1.0398819
## strata(tgroup)tgroup=1:HR_min 1.0081837
## strata(tgroup)tgroup=2:HR_min 1.0013060
## strata(tgroup)tgroup=1:Lactate_max 1.0946180
## strata(tgroup)tgroup=2:Lactate_max 0.9986499
## se(coef) z
## Age 0.0027499 12.550
## BUN_max 0.0013776 8.082
## Na_max 0.0078816 -5.133
## pH_min 0.1978059 -2.085
## Temp_max 0.0521644 -3.034
## Urine_min 0.0009464 -2.093
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.1694156 0.131
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2047092 -5.660
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.1311915 1.531
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 0.0000000 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.1898951 0.345
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.1780033 -1.725
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.1496993 3.650
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 0.0000000 NA
## strata(tgroup)tgroup=1:Albumin_min 0.0875372 -2.642
## strata(tgroup)tgroup=2:Albumin_min 0.0932299 0.276
## strata(tgroup)tgroup=1:Bilirubin_max 0.0081724 3.518
## strata(tgroup)tgroup=2:Bilirubin_max 0.0173879 -0.919
## strata(tgroup)tgroup=1:GCS_max 0.0157330 -8.147
## strata(tgroup)tgroup=2:GCS_max 0.0190784 -3.598
## strata(tgroup)tgroup=1:HCO3_min 0.0117341 -0.283
## strata(tgroup)tgroup=2:HCO3_min 0.0123778 3.159
## strata(tgroup)tgroup=1:HR_min 0.0032554 2.504
## strata(tgroup)tgroup=2:HR_min 0.0038581 0.338
## strata(tgroup)tgroup=1:Lactate_max 0.0202818 4.457
## strata(tgroup)tgroup=2:Lactate_max 0.0342960 -0.039
## Pr(>|z|)
## Age < 0.0000000000000002
## BUN_max 0.000000000000000636
## Na_max 0.000000285293278950
## pH_min 0.037042
## Temp_max 0.002410
## Urine_min 0.036316
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.896134
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.000000015146402643
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.125752
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.730037
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.084477
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.000263
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.008249
## strata(tgroup)tgroup=2:Albumin_min 0.782708
## strata(tgroup)tgroup=1:Bilirubin_max 0.000434
## strata(tgroup)tgroup=2:Bilirubin_max 0.358295
## strata(tgroup)tgroup=1:GCS_max 0.000000000000000372
## strata(tgroup)tgroup=2:GCS_max 0.000320
## strata(tgroup)tgroup=1:HCO3_min 0.776925
## strata(tgroup)tgroup=2:HCO3_min 0.001581
## strata(tgroup)tgroup=1:HR_min 0.012291
## strata(tgroup)tgroup=2:HR_min 0.735142
## strata(tgroup)tgroup=1:Lactate_max 0.000008293318325089
## strata(tgroup)tgroup=2:Lactate_max 0.968577
##
## Age ***
## BUN_max ***
## Na_max ***
## pH_min *
## Temp_max **
## Urine_min *
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 ***
## ICUTypeMedical ICU:strata(tgroup)tgroup=1
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 .
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 ***
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2
## strata(tgroup)tgroup=1:Albumin_min **
## strata(tgroup)tgroup=2:Albumin_min
## strata(tgroup)tgroup=1:Bilirubin_max ***
## strata(tgroup)tgroup=2:Bilirubin_max
## strata(tgroup)tgroup=1:GCS_max ***
## strata(tgroup)tgroup=2:GCS_max ***
## strata(tgroup)tgroup=1:HCO3_min
## strata(tgroup)tgroup=2:HCO3_min **
## strata(tgroup)tgroup=1:HR_min *
## strata(tgroup)tgroup=2:HR_min
## strata(tgroup)tgroup=1:Lactate_max ***
## strata(tgroup)tgroup=2:Lactate_max
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef)
## Age 1.0351
## BUN_max 1.0112
## Na_max 0.9604
## pH_min 0.6620
## Temp_max 0.8536
## Urine_min 0.9980
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 1.0224
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.3139
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 1.2225
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 1.0677
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.7356
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.7269
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 0.7935
## strata(tgroup)tgroup=2:Albumin_min 1.0260
## strata(tgroup)tgroup=1:Bilirubin_max 1.0292
## strata(tgroup)tgroup=2:Bilirubin_max 0.9842
## strata(tgroup)tgroup=1:GCS_max 0.8797
## strata(tgroup)tgroup=2:GCS_max 0.9337
## strata(tgroup)tgroup=1:HCO3_min 0.9967
## strata(tgroup)tgroup=2:HCO3_min 1.0399
## strata(tgroup)tgroup=1:HR_min 1.0082
## strata(tgroup)tgroup=2:HR_min 1.0013
## strata(tgroup)tgroup=1:Lactate_max 1.0946
## strata(tgroup)tgroup=2:Lactate_max 0.9986
## exp(-coef)
## Age 0.9661
## BUN_max 0.9889
## Na_max 1.0413
## pH_min 1.5106
## Temp_max 1.1715
## Urine_min 1.0020
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.9781
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 3.1856
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.8180
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.9366
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 1.3595
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 0.5791
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA
## strata(tgroup)tgroup=1:Albumin_min 1.2602
## strata(tgroup)tgroup=2:Albumin_min 0.9746
## strata(tgroup)tgroup=1:Bilirubin_max 0.9717
## strata(tgroup)tgroup=2:Bilirubin_max 1.0161
## strata(tgroup)tgroup=1:GCS_max 1.1368
## strata(tgroup)tgroup=2:GCS_max 1.0711
## strata(tgroup)tgroup=1:HCO3_min 1.0033
## strata(tgroup)tgroup=2:HCO3_min 0.9616
## strata(tgroup)tgroup=1:HR_min 0.9919
## strata(tgroup)tgroup=2:HR_min 0.9987
## strata(tgroup)tgroup=1:Lactate_max 0.9136
## strata(tgroup)tgroup=2:Lactate_max 1.0014
## lower .95 upper .95
## Age 1.0296 1.0407
## BUN_max 1.0085 1.0139
## Na_max 0.9456 0.9753
## pH_min 0.4492 0.9755
## Temp_max 0.7706 0.9455
## Urine_min 0.9962 0.9999
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=1 0.7335 1.4250
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=1 0.2102 0.4689
## ICUTypeMedical ICU:strata(tgroup)tgroup=1 0.9453 1.5809
## ICUTypeSurgical ICU:strata(tgroup)tgroup=1 NA NA
## ICUTypeCoronary Care Unit:strata(tgroup)tgroup=2 0.7359 1.5492
## ICUTypeCardiac Surgery Recovery Unit:strata(tgroup)tgroup=2 0.5189 1.0427
## ICUTypeMedical ICU:strata(tgroup)tgroup=2 1.2878 2.3158
## ICUTypeSurgical ICU:strata(tgroup)tgroup=2 NA NA
## strata(tgroup)tgroup=1:Albumin_min 0.6684 0.9421
## strata(tgroup)tgroup=2:Albumin_min 0.8547 1.2318
## strata(tgroup)tgroup=1:Bilirubin_max 1.0128 1.0458
## strata(tgroup)tgroup=2:Bilirubin_max 0.9512 1.0183
## strata(tgroup)tgroup=1:GCS_max 0.8530 0.9072
## strata(tgroup)tgroup=2:GCS_max 0.8994 0.9692
## strata(tgroup)tgroup=1:HCO3_min 0.9740 1.0199
## strata(tgroup)tgroup=2:HCO3_min 1.0150 1.0654
## strata(tgroup)tgroup=1:HR_min 1.0018 1.0146
## strata(tgroup)tgroup=2:HR_min 0.9938 1.0089
## strata(tgroup)tgroup=1:Lactate_max 1.0520 1.1390
## strata(tgroup)tgroup=2:Lactate_max 0.9337 1.0681
##
## Concordance= 0.749 (se = 0.009 )
## Likelihood ratio test= 577.1 on 24 df, p=<0.0000000000000002
## Wald test = 558.2 on 24 df, p=<0.0000000000000002
## Score (logrank) test = 607.6 on 24 df, p=<0.0000000000000002Final paragraph (very brief as per task) - summarising the most important findings of your final model - most important values from stats output - simple clinical interpretation ***
Findings of Final Model:
Save, knit and submit
Reminder: don’t forget to save this file, to knit it to check that everything works, and then submit via the drop box in OpenLearning.
Submit your assignment
When you have finished, and are satisfied with your assignment solutions, and this file knits without errors and the output looks the way you want, then you should submit via the drop box in OpenLearning.
Problems?
If you encounter problems with any part of the process described above, please contact the course convenor via OpenLearning as soon as possible so that the issues can be resolved in good time, and well before the assignment is due.
Additional Information
Each task attracts the indicated number of marks (out of a total of 30 marks for the assignment). The instructions are deliberately open-ended and less prescriptive than the individual assignments to allow you some latitude in what you do and how you go about the task. However, to complete the tasks and gain full marks, you only need to replicate or repeat the steps covered in the course - if you do most or all of the things described in the revalant chapters of the HDAT9600 course, full marks will be awarded.
Note also that with respect to the model fitting, there are no right or wrong answers when it comes to variable selection and other aspects of model specification. Deep understanding of the underlying medical concepts which govern patient treatment and outcomes in ICUs is not required or assumed, although you should try to gain some understanding of each variable using the links provided. You will not be marked down if your medical justifications are not exactly correct or complete, but do you best, and don’t hesitate to seek help from the course convenor.